Timed automata and the theory of real numbers
传播学理论——虚拟实在、沉浸及其文化意涵
那么，虚拟实在又是如何改变原型的呢？这包括两种情况。 其一，虚拟实在可以先于 原型而存在。例如， 如果利
用虚拟实在进行飞机设 计，原型就建立在 虚拟实在的基础 上。或许人们会 强调虚拟实在是 对已有 "原型 "的组合 ，但虚 拟实在与既往的设计和模型的差别在 于，虚拟实在是一种精确 可变的预处理或预制造，在 制造原型的过程中可 以随时
完全由设计者规定的单向生成过程， 而需要依据不同的使用者 的主观感受进行调节。换言 之，使用者本身也是 设计者 之一，而许多设计者也常常作为使用 者以改进其设计。由于数 字化处理可以及时修正调节 ，虚拟实在被建构成 为一种 开放性的人工实在。
3．虚拟的语义分析 作为人工实在，以往的人造物多为自然的模仿物或能够与自 然物融合的人工创造物， 除了固执神创论者 之外，
虚拟环境中的感官沉浸。
（5）遥在（telepresence）。虚拟实在能够使人实时地以远程的方式于某处出场，即虚拟出场。此时，出场相当于" 在场"，即你能够在现场之外实时地感知现场，并有效地进行某种操作。
（6）全身沉浸。这是一种不需要人体传感器的方式，摄像机和监视器实时地跟踪人的身体，将人体的运动输入到 计算机中，人的影像被投影到计算机界面上，这使得人通过观察他的投影的位置，直接与计算机中的图形物体（图片、
改变原有设计，使制造成为一种开放 性的制造。其二，虚拟实 在能够改变人们对原型的认 识。正如影视中的色 彩会影 响到流行色、 "高保真 "的音乐使 我们不满意没有 音响的音乐会一 样，虚拟实在会 使我们反过来以 它为标准评价 原型， 结果必然改变我们对原型的感知。
Nuttx操作系统进程切换调度实时性的形式化验证
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uppaal-tutorial
A Tutorial on Uppaal4.0Updated November28,2006Gerd Behrmann,Alexandre David,and Kim rsenDepartment of Computer Science,Aalborg University,Denmark{behrmann,adavid,kgl}@cs.auc.dk.Abstract.This is a tutorial paper on the tool Uppaal.Its goal is to bea short introduction on theflavour of timed automata implemented inthe tool,to present its interface,and to explain how to use the tool.Thecontribution of the paper is to provide reference examples and modellingpatterns.1IntroductionUppaal is a toolbox for verification of real-time systems jointly developed by Uppsala University and Aalborg University.It has been applied successfully in case studies ranging from communication protocols to multimedia applications [35,55,24,23,34,43,54,44,30].The tool is designed to verify systems that can be modelled as networks of timed automata extended with integer variables,struc-tured data types,user defined functions,and channel synchronisation.Thefirst version of Uppaal was released in1995[52].Since then it has been in constant development[21,5,13,10,26,27].Experiments and improvements in-clude data structures[53],partial order reduction[20],a distributed version of Uppaal[17,9],guided and minimal cost reachability[15,51,16],work on UML Statecharts[29],acceleration techniques[38],and new data structures and memory reductions[18,14].Version4.0[12]brings symmetry reduction[36], the generalised sweep-line method[49],new abstraction techniques[11],priori-ties[28],and user defined functions to the mainstream.Uppaal has also gen-erated related Ph.D.theses[50,57,45,56,19,25,32,8,31].It features a Java user interface and a verification engine written in C++.It is freely available at /.This tutorial covers networks of timed automata and theflavour of timed automata used in Uppaal in section2.The tool itself is described in section3, and three extensive examples are covered in sections4,5,and6.Finally,section7 introduces common modelling patterns often used with Uppaal.2Timed Automata in UppaalThe model-checker Uppaal is based on the theory of timed automata[4](see[42] for automata theory)and its modelling language offers additional features such as bounded integer variables and urgency.The query language of Uppaal,usedto specify properties to be checked,is a subset of TCTL (timed computation tree logic)[39,3].In this section we present the modelling and the query languages of Uppaal and we give an intuitive explanation of time in timed automata.2.1The Modelling LanguageNetworks of Timed Automata A timed automaton is a finite-state machine extended with clock variables.It uses a dense-time model where a clock variable evaluates to a real number.All the clocks progress synchronously.In Uppaal ,a system is modelled as a network of several such timed automata in parallel.The model is further extended with bounded discrete variables that are part of the state.These variables are used as in programming languages:They are read,written,and are subject to common arithmetic operations.A state of the system is defined by the locations of all automata,the clock values,and the values of the discrete variables.Every automaton may fire an edge (sometimes misleadingly called a transition)separately or synchronise with another automaton 1,which leads to a new state.Figure 1(a)shows a timed automaton modelling a simple lamp.The lamp has three locations:off ,low ,and bright .If the user presses a button,i.e.,synchronises with press?,then the lamp is turned on.If the user presses the button again,the lamp is turned off.However,if the user is fast and rapidly presses the button twice,the lamp is turned on and becomes bright.The user model is shown in Fig.1(b).The user can press the button randomly at any time or even not press the button at all.The clock y of the lamp is used to detect if the user was fast (y <5)or slow (y >=5).press?‚‚‚‚‚press!(a)Lamp.(b)User.Fig.1.The simple lamp example.We give the basic definitions of the syntax and semantics for the basic timed automata.In the following we will skip the richer flavour of timed automata supported in Uppaal ,i.e.,with integer variables and the extensions of urgent and committed locations.For additional information,please refer to the helpmenu inside the tool.We use the following notations:C is a set of clocks and B (C )is the set of conjunctions over simple conditions of the form x ⊲⊳c or x −y ⊲⊳c ,where x,y ∈C ,c ∈N and ⊲⊳∈{<,≤,=,≥,>}.A timed automaton is a finite directed graph annotated with conditions over and resets of non-negative real valued clocks.Definition 1(Timed Automaton (TA)).A timed automaton is a tuple (L,l 0,C,A,E,I ),where L is a set of locations,l 0∈L is the initial location,C is the set of clocks,A is a set of actions,co-actions and the internal τ-action,E ⊆L ×A ×B (C )×2C ×L is a set of edges between locations with an action,a guard and a set of clocks to be reset,and I :L →B (C )assigns invariants to locations. In the previous example on Fig.1,y:=0is the reset of the clock y ,and the labels press?and press!denote action–co-action (channel synchronisations here).We now define the semantics of a timed automaton.A clock valuation is a function u :C →R ≥0from the set of clocks to the non-negative reals.Let R C be the set of all clock valuations.Let u 0(x )=0for all x ∈C .We will abuse the notation by considering guards and invariants as sets of clock valuations,writing u ∈I (l )to mean that u satisfies I (l ).0000000001111111110001110000000000000000000000000000000000000000000000001111111111111111111111111111111111111111111111110000000000000000000000000000000000000000000000000000000011111111111111111111111111111111111111111111111111111111000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110000111100001111<B,x=1><A,x=2><A,x=3><A,x=3>action transition delay(+1) transition delay(+2) transition state: <A,x=1>actiontransitionOK invalid action transition invalid state: invariant x<3 violatedFig.2.Semantics of TA:different transitions from a given initial state.Definition 2(Semantics of TA).Let (L,l 0,C,A,E,I )be a timed automaton.The semantics is defined as a labelled transition system S,s 0,→ ,where S ⊆L ×R C is the set of states,s 0=(l 0,u 0)is the initial state,and →⊆S ×(R ≥0∪A )×S is the transition relation such that:–(l,u )d−→(l,u +d )if ∀d ′:0≤d ′≤d =⇒u +d ′∈I (l ),and –(l,u )a −→(l ′,u ′)if there exists e =(l,a,g,r,l ′)∈E s.t.u ∈g ,u ′=[r →0]u ,and u ′∈I (l ′),3where for d∈R≥0,u+d maps each clock x in C to the value u(x)+d,and [r→0]u denotes the clock valuation which maps each clock in r to0and agrees with u over C\r. Figure2illustrates the semantics of TA.From a given initial state,we can choose to take an action or a delay transition(different values here).Depending of the chosen delay,further actions may be forbidden.Timed automata are often composed into a network of timed automata over a common set of clocks and actions,consisting of n timed automata A i= (L i,l0i,C,A,E i,I i),1≤i≤n.A location vector is a vector¯l=(l1,...,l n). We compose the invariant functions into a common function over location vec-tors I(¯l)=∧i I i(l i).We write¯l[l′i/l i]to denote the vector where the i th element l i of¯l is replaced by l′i.In the following we define the semantics of a network of timed automata.Definition3(Semantics of a network of Timed Automata).Let A i= (L i,l0i,C,A,E i,I i)be a network of n timed automata.Let¯l0=(l01,...,l0n)be the initial location vector.The semantics is defined as a transition system S,s0,→ , where S=(L1×···×L n)×R C is the set of states,s0=(¯l0,u0)is the initial state,and→⊆S×S is the transition relation defined by:–(¯l,u)d−→(¯l,u+d)if∀d′:0≤d′≤d=⇒u+d′∈I(¯l).−−→l′i s.t.u∈g,–(¯l,u)a−→(¯l[l′i/l i],u′)if there exists l iτgru′=[r→0]u and u′∈I(¯l[l′i/l i]).–(¯l,u)a−→(¯l[l′j/l j,l′i/l i],u′)if there exist l i c?g i r i−−−−→l′i and−−−−→l′j s.t.u∈(g i∧g j),u′=[r i∪r j→0]u and u′∈I(¯l[l′j/l j,l′i/l i]).l j c!g j r jAs an example of the semantics,the lamp in Fig.1may have the follow-ing states(we skip the user):(Lamp.off,y=0)→(Lamp.off,y=3)→(Lamp.low,y=0)→(Lamp.low,y=0.5)→(Lamp.bright,y=0.5)→(Lamp.bright,y=1000)...Timed Automata in Uppaal The Uppaal modelling language extends timed automata with the following additional features(see Fig.3:Templates automata are defined with a set of parameters that can be of any type(e.g.,int,chan).These parameters are substituted for a given argument in the process declaration.Constants are declared as const name value.Constants by definition cannot be modified and must have an integer value.Bounded integer variables are declared as int[min,max]name,where min and max are the lower and upper bound,respectively.Guards,invariants,and assignments may contain expressions ranging over bounded integer variables.The bounds are checked upon verification and violating a bound leads to an invalid state that is discarded(at run-time).If the bounds are omitted,the default range of-32768to32768is used.4Fig.3.Declarations of a constant and a variable,and illustration of some of the channel synchronisations between two templates of the train gate example of Section4,and some committed locations.5Binary synchronisation channels are declared as chan c.An edge labelled with c!synchronises with another labelled c?.A synchronisation pair is chosen non-deterministically if several combinations are enabled. Broadcast channels are declared as broadcast chan c.In a broadcast syn-chronisation one sender c!can synchronise with an arbitrary number of receivers c?.Any receiver than can synchronise in the current state must do so.If there are no receivers,then the sender can still execute the c!action,i.e.broadcast sending is never blocking.Urgent synchronisation channels are declared by prefixing the channel decla-ration with the keyword urgent.Delays must not occur if a synchronisation transition on an urgent channel is enabled.Edges using urgent channels for synchronisation cannot have time constraints,i.e.,no clock guards. Urgent locations are semantically equivalent to adding an extra clock x,that is reset on all incoming edges,and having an invariant x<=0on the location.Hence,time is not allowed to pass when the system is in an urgent location. Committed locations are even more restrictive on the execution than urgent locations.A state is committed if any of the locations in the state is commit-ted.A committed state cannot delay and the next transition must involve an outgoing edge of at least one of the committed locations.Arrays are allowed for clocks,channels,constants and integer variables.They are defined by appending a size to the variable name,e.g.chan c[4];clock a[2];int[3,5]u[7];.Initialisers are used to initialise integer variables and arrays of integer vari-ables.For instance,int i=2;or int i[3]={1,2,3};.Record types are declared with the struct construct like in C.Custom types are defined with the C-like typedef construct.You can define any custom-type from other basic types such as records.User functions are defined either globally or locally to templates.Template parameters are accessible from local functions.The syntax is similar to C except that there is no pointer.C++syntax for references is supported for the arguments only.Expressions in Uppaal Expressions in Uppaal range over clocks and integer variables.The BNF is given in Fig.33in the appendix.Expressions are used with the following labels:Select A select label contains a comma separated list of name:type expressions where name is a variable name and type is a defined type(built-in or custom).These variables are accessible on the associated edge only and they will takea non-deterministic value in the range of their respective types.Guard A guard is a particular expression satisfying the following conditions: it is side-effect free;it evaluates to a boolean;only clocks,integer variables, and constants are referenced(or arrays of these types);clocks and clock differences are only compared to integer expressions;guards over clocks are essentially conjunctions(disjunctions are allowed over integer conditions).A guard may call a side-effect free function that returns a bool,although clock constraints are not supported in such functions.6Synchronisation A synchronisation label is either on the form Expression!or Expression?or is an empty label.The expression must be side-effect free, evaluate to a channel,and only refer to integers,constants and channels. Update An update label is a comma separated list of expressions with a side-effect;expressions must only refer to clocks,integer variables,and constants and only assign integer values to clocks.They may also call functions. Invariant An invariant is an expression that satisfies the following conditions:it is side-effect free;only clock,integer variables,and constants are referenced;it is a conjunction of conditions of the form x<e or x<=e where x is a clock reference and e evaluates to an integer.An invariant may call a side-effect free function that returns a bool,although clock constraints are not supported in such functions.2.2The Query LanguageThe main purpose of a model-checker is verify the model w.r.t.a requirement specification.Like the model,the requirement specification must be expressed in a formally well-defined and machine readable language.Several such logics exist in the scientific literature,and Uppaal uses a simplified version of TCTL. Like in TCTL,the query language consists of path formulae and state formulae.2 State formulae describe individual states,whereas path formulae quantify over paths or traces of the model.Path formulae can be classified into reachability, safety and liveness.Figure4illustrates the different path formulae supported by Uppaal.Each type is described below.State Formulae A state formula is an expression(see Fig.33)that can be evaluated for a state without looking at the behaviour of the model.For instance, this could be a simple expression,like i==7,that is true in a state whenever i equals7.The syntax of state formulae is a superset of that of guards,i.e.,a state formula is a side-effect free expression,but in contrast to guards,the use of disjunctions is not restricted.It is also possible to test whether a particular process is in a given location using an expression on the form P.l,where P is a process and l is a location.In Uppaal,deadlock is expressed using a special state formula(although this is not strictly a state formula).The formula simply consists of the keyword deadlock and is satisfied for all deadlock states.A state is a deadlock state if there are no outgoing action transitions neither from the state itself or any of its delay successors.Due to current limitations in Uppaal,the deadlock state formula can only be used with reachability and invariantly path formulae(see below).Reachability Properties Reachability properties are the simplest form of properties.They ask whether a given state formula,ϕ,possibly can be satisfied3Notice that A ϕ=¬E3¬ϕ8there should exist a maximal path such thatϕis always true.4In Uppaal we write A[]ϕand E[]ϕ,respectively.Liveness Properties Liveness properties are of the form:something will even-tually happen,e.g.when pressing the on button of the remote control of the television,then eventually the television should turn on.Or in a model of a communication protocol,any message that has been sent should eventually be received.In its simple form,liveness is expressed with the path formula A3ϕ,mean-ingϕis eventually satisfied.5The more useful form is the leads to or response property,writtenϕ ψwhich is read as wheneverϕis satisfied,then eventu-allyψwill be satisfied,e.g.whenever a message is sent,then eventually it will be received.6In Uppaal these properties are written as A<>ϕandϕ-->ψ, respectively.2.3Understanding TimeInvariants and Guards Uppaal uses a continuous time model.We illustrate the concept of time with a simple example that makes use of an observer.Nor-mally an observer is an add-on automaton in charge of detecting events without changing the observed system.In our case the clock reset(x:=0)is delegated to the observer for illustration purposes.Figure5shows thefirst model with its observer.We have two automata in parallel.Thefirst automaton has a self-loop guarded by x>=2,x being a clock,that synchronises on the channel reset with the second automaton.The second automaton,the observer,detects when the self loop edge is taken with the location taken and then has an edge going back to idle that resets the clock x.We moved the reset of x from the self loop to the observer only to test what happens on the transition before the reset.Notice that the location taken is committed(marked c)to avoid delay in that location.The following properties can be verified in Uppaal(see section3for an overview of the interface).Assuming we name the observer automaton Obs,we have:–A[]Obs.taken imply x>=2:all resets offx will happen when x is above2.This query means that for all reachable states,being in the locationObs.taken implies that x>=2.–E<>Obs.idle and x>3:this property requires,that it is possible to reach-able state where Obs is in the location idle and x is bigger than3.Essentially we check that we may delay at least3time units between resets.The result would have been the same for larger values like30000,since there are no invariants in this model.x>=2reset!‚‚‚‚‚246824"time"c l o c k x (a)Test.(b)Observer.(c)Behaviour:one possible run.Fig.5.First example with anobserver.x>=2reset!246824"time"c l o c k x(a)Test.(b)Updated behaviour with an invariant.Fig.6.Updated example with an invariant.The observer is the same as in Fig.5and is not shown here.We update the first model and add an invariant to the location loop ,as shown in Fig.6.The invariant is a progress condition:the system is not allowed to stay in the state more than 3time units,so that the transition has to be taken and the clock reset in our example.Now the clock x has 3as an upper bound.The following properties hold:–A[]Obs.taken imply (x>=2and x<=3)shows that the transition is takenwhen x is between 2and 3,i.e.,after a delay between 2and 3.–E<>Obs.idle and x>2:it is possible to take the transition when x is be-tween 2and 3.The upper bound 3is checked with the next property.–A[]Obs.idle imply x<=3:to show that the upper bound is respected.The former property E<>Obs.idle and x>3no longer holds.Now,if we remove the invariant and change the guard to x>=2and x<=3,you may think that it is the same as before,but it is not!The system has no progress condition,just a new condition on the guard.Figure 7shows what happens:the system may take the same transitions as before,but deadlock may also occur.The system may be stuck if it does not take the transition after 3time units.In fact,the system fails the property A[]not deadlock .The property A[]Obs.idle imply x<=3does not hold any longer and the deadlock can also be illustrated by the property A[]x>3imply not Obs.taken ,i.e.,after 3time units,the transition is not taken any more.10x>=2 && x<=3reset!246824"time"c l o c k x(a)Test.(b)Updated behaviour with a guard and no invariant.Fig.7.Updated example with a guard and no invariant.P0P1P2Fig.8.Automata in parallel with normal,urgent and commit states.The clocks are local,i.e.,P0.x and P1.x are two different clocks.Committed and Urgent Locations There are three different types of loca-tions in Uppaal :normal locations with or without invariants (e.g.,x<=3in the previous example),urgent locations,and committed locations.Figure 8shows 3automata to illustrate the difference.The location marked u is urgent and the one marked c is committed.The clocks are local to the automata,i.e.,x in P0is different from x in P1.To understand the difference between normal locations and urgent locations,we can observe that the following properties hold:–E<>P0.S1and P0.x>0:it is possible to wait in S1of P0.–A[]P1.S1imply P1.x==0:it is not possible to wait in S1of P1.An urgent location is equivalent to a location with incoming edges reseting a designated clock y and labelled with the invariant y<=0.Time may not progress in an urgent state,but interleavings with normal states are allowed.A committed location is more restrictive:in all the states where P2.S1is active (in our example),the only possible transition is the one that fires the edge outgoing from P2.S1.A state having a committed location active is said to11be committed:delay is not allowed and the committed location must be left in the successor state(or one of the committed locations if there are several ones). 3Overview of the Uppaal ToolkitUppaal uses a client-server architecture,splitting the tool into a graphical user interface and a model checking engine.The user interface,or client,is imple-mented in Java and the engine,or server,is compiled for different platforms (Linux,Windows,Solaris).7As the names suggest,these two components may be run on different machines as they communicate with each other via TCP/IP. There is also a stand-alone version of the engine that can be used on the com-mand line.3.1The Java ClientThe idea behind the tool is to model a system with timed automata using a graphical editor,simulate it to validate that it behaves as intended,andfinally to verify that it is correct with respect to a set of properties.The graphical interface(GUI)of the Java client reflects this idea and is divided into three main parts:the editor,the simulator,and the verifier,accessible via three“tabs”. The Editor A system is defined as a network of timed automata,called pro-cesses in the tool,put in parallel.A process is instantiated from a parameterised template.The editor is divided into two parts:a tree pane to access the different templates and declarations and a drawing canvas/text editor.Figure9shows the editor with the train gate example of section4.Locations are labelled with names and invariants and edges are labelled with guard conditions(e.g.,e==id), synchronisations(e.g.,go?),and assignments(e.g.,x:=0).The tree on the left hand side gives access to different parts of the system description:Global declaration Contains global integer variables,clocks,synchronisation channels,and constants.Templates Train,Gate,and IntQueue are different parameterised timed au-tomata.A template may have local declarations of variables,channels,and constants.Process assignments Templates are instantiated into processes.The process assignment section contains declarations for these instances.System definition The list of processes in the system.The syntax used in the labels and the declarations is described in the help system of the tool.The local and global declarations are shown in Fig.10.The graphical syntax is directly inspired from the description of timed automata in section2.12Fig.9.The train automaton of the train gate example.The select button is activated in the tool-bar.In this mode the user can move locations and edges or edit labels. The other modes are for adding locations,edges,and vertices on edges(called nails).A new location has no name by default.Two textfields allow the user to define the template name and its eful trick:The middle mouse button is a shortcut for adding new elements,i.e.pressing it on the canvas,a location,or edge adds a new location,edge,or nail,respectively.The Simulator The simulator can be used in three ways:the user can run the system manually and choose which transitions to take,the random mode can be toggled to let the system run on its own,or the user can go through a trace (saved or imported from the verifier)to see how certain states are reachable. Figure11shows the simulator.It is divided into four parts:The control part is used to choose andfire enabled transitions,go through a trace,and toggle the random simulation.The variable view shows the values of the integer variables and the clock con-straints.Uppaal does not show concrete states with actual values for the clocks.Since there are infinitely many of such states,Uppaal instead shows sets of concrete states known as symbolic states.All concrete states in a sym-bolic state share the same location vector and the same values for discretevariables.The possible values of the clocks is described by a set of con-Fig.10.The different local and global declarations of the train gate example.We superpose several screen-shots of the tool to show the declarations in a compact manner.straints.The clock validation in the symbolic state are exactly those that satisfy all constraints.The system view shows all instantiated automata and active locations of the current state.The message sequence chart shows the synchronisations between the differ-ent processes as well as the active locations at every step.The Verifier The verifier“tab”is shown in Fig.12.Properties are selectable in the Overview list.The user may model-check one or several properties,8insert or remove properties,and toggle the view to see the properties or the comments in the list.When a property is selected,it is possible to edit its definition(e.g., E<>Train1.Cross and Train2.Stop...)or comments to document what the property means informally.The Status panel at the bottom shows the commu-nication with the server.When trace generation is enabled and the model-checkerfinds a trace,the user is asked if she wants to import it into the simulator.Satisfied properties are marked green and violated ones red.In case either an over approximation or an under approximation has been selected in the options menu,then it may happen that the verification is inconclusive with the approximation used.In that casethe properties are marked yellow.Fig.11.View of the simulator tab for the train gate example.The interpretation of the constraint system in the variable panel depends on whether a transition in the transition panel is selected or not.If no transition is selected,then the constrain system shows all possible clock valuations that can be reached along the path.If a transition is selected,then only those clock valuations from which the transition can be taken are shown.Keyboard bindings for navigating the simulator without the mouse can be found in the integrated help system.3.2The Stand-alone VerifierWhen running large verification tasks,it is often cumbersome to execute these from inside the GUI.For such situations,the stand-alone command line verifier called verifyta is more appropriate.It also makes it easy to run the verification on a remote UNIX machine with memory to spare.It accepts command line arguments for all options available in the GUI,see Table3in the appendix.4Example1:The Train Gate4.1DescriptionThe train gate example is distributed with Uppaal.It is a railway control system which controls access to a bridge for several trains.The bridge is a critical shared resource that may be accessed only by one train at a time.The system is defined as a number of trains(assume4for this example)and a controller.A train can not be stopped instantly and restarting also takes time.Therefor,there are timing constraints on the trains before entering the bridge.When approaching,15。
伽达默尔哲学的七个关键术语
伽达默尔哲学的七个关键术语本文系帕尔默教授2002年6月27日在安徽师范大学作的学术报告，由江涛译为中文，潘德荣校。
【作者简介】R.E.帕尔默(1933-)，男，美国伊利诺伊州麦克默里大学哲学教授，从事诠释学教学与研究30多年，他于1960年写的《诠释学》，系该学科的标准教材。
【内容提要】“存在之显现”是伽达默尔的真理观念。
“时间性”指的是通过语言性、书写性、和诗歌的奇迹，产生了文本战胜历史“时间”而具有“同时性”的奇迹。
“实践智慧”是伦理方式选择善的理智。
“应用”的意思是当我们理解过去的某件事物时，我们同样领会它在今天是如何应用的“传统”是指我们在语言中继承下来的态度和方法，在我们试图弄懂任何事物时都会在我们的意识中发生作用，而“效果历史意识”是一种历史总结在发挥作用的意识。
语言最典型地生存于交谈、问答、对话的平等交换之中。
使人类团结在一起的节日庆典是真正交流的基础。
【英文摘要】“Emergency into being”is Gadamer's concept of truth.Zeitlichreit(timeliness)refers to the fact that though the miracle of language,writtenness and poetry,comes the miracle of“simutaneity”in a text that overcomes historical time.Phronoesis (practicle wisdom) is the intelligence that chooses the Good in an ethical way.Applicatio(application) means that when we understand something in the past,and we also see how it applies at present.Tradition refers to our seeing that an attitude and way of seeing that we inherit in our language is at work inour consciousness as we attempt to understand anything,while wirkungschichttiches Buwusstsein (effect consciousness) is a consciousnes in which history is always working.For Gadamer language lives most typically in the give and take of conversation,of question and answer,of dialogue.Gadamer also argues that the rituals and rites that hold humanbeings together in solitarity are their basis for real communication.【关键词】真理/实践智慧/应用/传统和效果历史意识/谈话/团结/Wahrheit(truth)/Zeitlichkeit(timeliness)/Pronolisis(practicalwisdom)/Applicatio(application)/Tradition and wirkungs geschichtliches(tradition and effect historical consciousness)/Gespraech(dialogue)/Solidaritaet(unity)一非常荣幸应我的朋友潘德荣邀请来和你们谈谈伽达默尔的诠释哲学，谢谢大家!在1999年退休前，当我在我的学院讲授“儒教、道教和禅宗”这门课程时[1]，我试图在第一堂课中通过较详细地给一些关键术语下定义来解释儒家学说。
笛卡尔的本体论之争
笛卡尔的本体论之争首先周一公布2001年6月18日;实质性修改太阳2006年10月15日笛卡尔的本体论（或先验）的论点，既是哲学的一个最迷人，他的理解方面的不足。
论据与魅力源于努力证明神的存在，从简单的处所，但功能强大。
存在是产生立即从清晰和明确的想法是一个无比完美。
讽刺的是，简单的说法也产生了一些误读，加剧了部分由笛卡尔没有一套单一版本。
该声明的论点主要出现在第五沉思。
这种说法因果来得早在接踵而至的一个神的存在，沉思在第三，不同的证据提出问题的两项之间的秩序和关系。
重复笛卡尔哲学原理，包括本体论争论的几个文本等中央。
他还辩解首先由一些主要的知识分子，他在一天，严厉打击反对第二次回复，和第五。
笛卡尔不是第一位哲学家，制订一个本体论的论点。
一个早期版本的说法已大力安瑟伦辩护圣在11世纪，然后圣托马斯阿奎那批评由当代），后来被命名为Gaunilo和尚（安瑟伦（尽管他的言论是针对然而，另一个版本参数）。
阿奎那的批评被视为如此具有破坏性，本体论的争论了数百年死亡。
它的出现，作为一个同时代的惊喜笛卡尔，他应该试图复活它。
虽然他声称没有被证明的熟悉安瑟伦的版本，笛卡尔似乎他自己的工艺参数，以阻止传统的反对。
尽管相似之处，笛卡尔的论点的版本不同于安瑟伦方式在重要的。
后者的版本被认为要从定义这个词的含义“上帝”，上帝是一个被一大于不能设想。
笛卡尔的观点相反，中，主要是基于两个他的哲学的中心原则-天生的思想理论和学说明确的印象和独特的。
他声称不依赖于上帝的任意定义，而是一种天生的想法，其内容是“的。
” 笛卡尔的版本也非常简单。
神的存在是直接从推断的事实，有必要存在的想法是包含在一个清晰而鲜明的超级完美的存在。
事实上，在一些场合，他建议，所谓的本体论“的论调”是不是一个正式的哲学偏见的证据，而是在所有不言而喻的公理直观地掌握了一个心灵的自由。
笛卡尔的本体论的争论相比往往以几何论证，认为有必要存在的想法不能排除再从神比事实平等的角度，其角度，例如两权，可以被排除在一个三角形的想法。
终极理论 物理学术语
终极理论物理学术语终极理论英语名称是the Theory of Ultimate，在物理学中，终极理论又称万有理论，是二十世纪六十年代以后，量子论物理学家们提出的一个标准模型理论。
物理学家们即将把引力、电磁力与原子核力用单独一项数学定律来描述。
那么万物的理论是什么？万物理论是科学界广泛使用的术语。
实际上，有一个著名物理学家史蒂芬·霍金教授的传记，以该理论命名。
如果你认为万物理论是对物理学中所有问题的解答，并且它将标志着人类长期以来对宇宙的好奇心的终结，那么你是错的。
万物理论并不能解决所有问题，这就像可以推导出其他一切的基本定律一样。
例如，库仑定律是静电的基本定律，可以从高斯定理中得出，反之亦然。
实际上，科学家说，万物理论仅仅是个开始。
从技术上讲，万物理论是一个假设框架，涵盖了宇宙的所有物理方面。
简而言之，就是极限理论告诉我们宇宙是如何工作的。
现在，让我们深入研究所有重要的理论以了解其含义。
描述物理学万物理论都有哪些最初描述万物理论的是20世纪的量子力学和相对论，在自远古时代以来，人类一直对它们的存在及其在宇宙中的地位感到好奇。
但是，将自然的工作描述为基本定律并不总是哲学家的趋势。
可能，第一个提供描述自然规律的理论框架的哲学家是阿基米德原理中的阿基米德，阿基米德原理是流体力学的基本定律。
我们可以清楚地描述某些物理现象，但是万物理论的主要目的是使它们统一。
例如，我们可以使用爱因斯坦的相对论通论来定义重力，并可以使用麦克斯韦定律来定义电磁力，但是当我们试图统一它们时就会出现主要问题。
爱因斯坦竭尽全力统一这两个基本力量，但他失败了。
假设我们需要创建一个融合的电引力理论。
我们该怎么做？一个理论必须是极简主义的，这意味着我们需要创建可以结合重力和电磁学的定律。
在我们建立了可以成功地结合重力和电磁学并定义了电引力各个方面的定律之后，我们就成功地发现了一个新理论。
现在，这种新理论具有导出电磁定律和重力定律的能力，这使其成为非常重要的理论。
OSHA现场作业手册说明书
DIRECTIVE NUMBER: CPL 02-00-150 EFFECTIVE DATE: April 22, 2011 SUBJECT: Field Operations Manual (FOM)ABSTRACTPurpose: This instruction cancels and replaces OSHA Instruction CPL 02-00-148,Field Operations Manual (FOM), issued November 9, 2009, whichreplaced the September 26, 1994 Instruction that implemented the FieldInspection Reference Manual (FIRM). The FOM is a revision of OSHA’senforcement policies and procedures manual that provides the field officesa reference document for identifying the responsibilities associated withthe majority of their inspection duties. This Instruction also cancels OSHAInstruction FAP 01-00-003 Federal Agency Safety and Health Programs,May 17, 1996 and Chapter 13 of OSHA Instruction CPL 02-00-045,Revised Field Operations Manual, June 15, 1989.Scope: OSHA-wide.References: Title 29 Code of Federal Regulations §1903.6, Advance Notice ofInspections; 29 Code of Federal Regulations §1903.14, Policy RegardingEmployee Rescue Activities; 29 Code of Federal Regulations §1903.19,Abatement Verification; 29 Code of Federal Regulations §1904.39,Reporting Fatalities and Multiple Hospitalizations to OSHA; and Housingfor Agricultural Workers: Final Rule, Federal Register, March 4, 1980 (45FR 14180).Cancellations: OSHA Instruction CPL 02-00-148, Field Operations Manual, November9, 2009.OSHA Instruction FAP 01-00-003, Federal Agency Safety and HealthPrograms, May 17, 1996.Chapter 13 of OSHA Instruction CPL 02-00-045, Revised FieldOperations Manual, June 15, 1989.State Impact: Notice of Intent and Adoption required. See paragraph VI.Action Offices: National, Regional, and Area OfficesOriginating Office: Directorate of Enforcement Programs Contact: Directorate of Enforcement ProgramsOffice of General Industry Enforcement200 Constitution Avenue, NW, N3 119Washington, DC 20210202-693-1850By and Under the Authority ofDavid Michaels, PhD, MPHAssistant SecretaryExecutive SummaryThis instruction cancels and replaces OSHA Instruction CPL 02-00-148, Field Operations Manual (FOM), issued November 9, 2009. The one remaining part of the prior Field Operations Manual, the chapter on Disclosure, will be added at a later date. This Instruction also cancels OSHA Instruction FAP 01-00-003 Federal Agency Safety and Health Programs, May 17, 1996 and Chapter 13 of OSHA Instruction CPL 02-00-045, Revised Field Operations Manual, June 15, 1989. This Instruction constitutes OSHA’s general enforcement policies and procedures manual for use by the field offices in conducting inspections, issuing citations and proposing penalties.Significant Changes∙A new Table of Contents for the entire FOM is added.∙ A new References section for the entire FOM is added∙ A new Cancellations section for the entire FOM is added.∙Adds a Maritime Industry Sector to Section III of Chapter 10, Industry Sectors.∙Revises sections referring to the Enhanced Enforcement Program (EEP) replacing the information with the Severe Violator Enforcement Program (SVEP).∙Adds Chapter 13, Federal Agency Field Activities.∙Cancels OSHA Instruction FAP 01-00-003, Federal Agency Safety and Health Programs, May 17, 1996.DisclaimerThis manual is intended to provide instruction regarding some of the internal operations of the Occupational Safety and Health Administration (OSHA), and is solely for the benefit of the Government. No duties, rights, or benefits, substantive or procedural, are created or implied by this manual. The contents of this manual are not enforceable by any person or entity against the Department of Labor or the United States. Statements which reflect current Occupational Safety and Health Review Commission or court precedents do not necessarily indicate acquiescence with those precedents.Table of ContentsCHAPTER 1INTRODUCTIONI.PURPOSE. ........................................................................................................... 1-1 II.SCOPE. ................................................................................................................ 1-1 III.REFERENCES .................................................................................................... 1-1 IV.CANCELLATIONS............................................................................................. 1-8 V. ACTION INFORMATION ................................................................................. 1-8A.R ESPONSIBLE O FFICE.......................................................................................................................................... 1-8B.A CTION O FFICES. .................................................................................................................... 1-8C. I NFORMATION O FFICES............................................................................................................ 1-8 VI. STATE IMPACT. ................................................................................................ 1-8 VII.SIGNIFICANT CHANGES. ............................................................................... 1-9 VIII.BACKGROUND. ................................................................................................. 1-9 IX. DEFINITIONS AND TERMINOLOGY. ........................................................ 1-10A.T HE A CT................................................................................................................................................................. 1-10B. C OMPLIANCE S AFETY AND H EALTH O FFICER (CSHO). ...........................................................1-10B.H E/S HE AND H IS/H ERS ..................................................................................................................................... 1-10C.P ROFESSIONAL J UDGMENT............................................................................................................................... 1-10E. W ORKPLACE AND W ORKSITE ......................................................................................................................... 1-10CHAPTER 2PROGRAM PLANNINGI.INTRODUCTION ............................................................................................... 2-1 II.AREA OFFICE RESPONSIBILITIES. .............................................................. 2-1A.P ROVIDING A SSISTANCE TO S MALL E MPLOYERS. ...................................................................................... 2-1B.A REA O FFICE O UTREACH P ROGRAM. ............................................................................................................. 2-1C. R ESPONDING TO R EQUESTS FOR A SSISTANCE. ............................................................................................ 2-2 III. OSHA COOPERATIVE PROGRAMS OVERVIEW. ...................................... 2-2A.V OLUNTARY P ROTECTION P ROGRAM (VPP). ........................................................................... 2-2B.O NSITE C ONSULTATION P ROGRAM. ................................................................................................................ 2-2C.S TRATEGIC P ARTNERSHIPS................................................................................................................................. 2-3D.A LLIANCE P ROGRAM ........................................................................................................................................... 2-3 IV. ENFORCEMENT PROGRAM SCHEDULING. ................................................ 2-4A.G ENERAL ................................................................................................................................................................. 2-4B.I NSPECTION P RIORITY C RITERIA. ..................................................................................................................... 2-4C.E FFECT OF C ONTEST ............................................................................................................................................ 2-5D.E NFORCEMENT E XEMPTIONS AND L IMITATIONS. ....................................................................................... 2-6E.P REEMPTION BY A NOTHER F EDERAL A GENCY ........................................................................................... 2-6F.U NITED S TATES P OSTAL S ERVICE. .................................................................................................................. 2-7G.H OME-B ASED W ORKSITES. ................................................................................................................................ 2-8H.I NSPECTION/I NVESTIGATION T YPES. ............................................................................................................... 2-8 V.UNPROGRAMMED ACTIVITY – HAZARD EVALUATION AND INSPECTION SCHEDULING ............................................................................ 2-9 VI.PROGRAMMED INSPECTIONS. ................................................................... 2-10A.S ITE-S PECIFIC T ARGETING (SST) P ROGRAM. ............................................................................................. 2-10B.S CHEDULING FOR C ONSTRUCTION I NSPECTIONS. ..................................................................................... 2-10C.S CHEDULING FOR M ARITIME I NSPECTIONS. ............................................................................. 2-11D.S PECIAL E MPHASIS P ROGRAMS (SEP S). ................................................................................... 2-12E.N ATIONAL E MPHASIS P ROGRAMS (NEP S) ............................................................................... 2-13F.L OCAL E MPHASIS P ROGRAMS (LEP S) AND R EGIONAL E MPHASIS P ROGRAMS (REP S) ............ 2-13G.O THER S PECIAL P ROGRAMS. ............................................................................................................................ 2-13H.I NSPECTION S CHEDULING AND I NTERFACE WITH C OOPERATIVE P ROGRAM P ARTICIPANTS ....... 2-13CHAPTER 3INSPECTION PROCEDURESI.INSPECTION PREPARATION. .......................................................................... 3-1 II.INSPECTION PLANNING. .................................................................................. 3-1A.R EVIEW OF I NSPECTION H ISTORY .................................................................................................................... 3-1B.R EVIEW OF C OOPERATIVE P ROGRAM P ARTICIPATION .............................................................................. 3-1C.OSHA D ATA I NITIATIVE (ODI) D ATA R EVIEW .......................................................................................... 3-2D.S AFETY AND H EALTH I SSUES R ELATING TO CSHO S.................................................................. 3-2E.A DVANCE N OTICE. ................................................................................................................................................ 3-3F.P RE-I NSPECTION C OMPULSORY P ROCESS ...................................................................................................... 3-5G.P ERSONAL S ECURITY C LEARANCE. ................................................................................................................. 3-5H.E XPERT A SSISTANCE. ........................................................................................................................................... 3-5 III. INSPECTION SCOPE. ......................................................................................... 3-6A.C OMPREHENSIVE ................................................................................................................................................... 3-6B.P ARTIAL. ................................................................................................................................................................... 3-6 IV. CONDUCT OF INSPECTION .............................................................................. 3-6A.T IME OF I NSPECTION............................................................................................................................................. 3-6B.P RESENTING C REDENTIALS. ............................................................................................................................... 3-6C.R EFUSAL TO P ERMIT I NSPECTION AND I NTERFERENCE ............................................................................. 3-7D.E MPLOYEE P ARTICIPATION. ............................................................................................................................... 3-9E.R ELEASE FOR E NTRY ............................................................................................................................................ 3-9F.B ANKRUPT OR O UT OF B USINESS. .................................................................................................................... 3-9G.E MPLOYEE R ESPONSIBILITIES. ................................................................................................. 3-10H.S TRIKE OR L ABOR D ISPUTE ............................................................................................................................. 3-10I. V ARIANCES. .......................................................................................................................................................... 3-11 V. OPENING CONFERENCE. ................................................................................ 3-11A.G ENERAL ................................................................................................................................................................ 3-11B.R EVIEW OF A PPROPRIATION A CT E XEMPTIONS AND L IMITATION. ..................................................... 3-13C.R EVIEW S CREENING FOR P ROCESS S AFETY M ANAGEMENT (PSM) C OVERAGE............................. 3-13D.R EVIEW OF V OLUNTARY C OMPLIANCE P ROGRAMS. ................................................................................ 3-14E.D ISRUPTIVE C ONDUCT. ...................................................................................................................................... 3-15F.C LASSIFIED A REAS ............................................................................................................................................. 3-16VI. REVIEW OF RECORDS. ................................................................................... 3-16A.I NJURY AND I LLNESS R ECORDS...................................................................................................................... 3-16B.R ECORDING C RITERIA. ...................................................................................................................................... 3-18C. R ECORDKEEPING D EFICIENCIES. .................................................................................................................. 3-18 VII. WALKAROUND INSPECTION. ....................................................................... 3-19A.W ALKAROUND R EPRESENTATIVES ............................................................................................................... 3-19B.E VALUATION OF S AFETY AND H EALTH M ANAGEMENT S YSTEM. ....................................................... 3-20C.R ECORD A LL F ACTS P ERTINENT TO A V IOLATION. ................................................................................. 3-20D.T ESTIFYING IN H EARINGS ................................................................................................................................ 3-21E.T RADE S ECRETS. ................................................................................................................................................. 3-21F.C OLLECTING S AMPLES. ..................................................................................................................................... 3-22G.P HOTOGRAPHS AND V IDEOTAPES.................................................................................................................. 3-22H.V IOLATIONS OF O THER L AWS. ....................................................................................................................... 3-23I.I NTERVIEWS OF N ON-M ANAGERIAL E MPLOYEES .................................................................................... 3-23J.M ULTI-E MPLOYER W ORKSITES ..................................................................................................................... 3-27 K.A DMINISTRATIVE S UBPOENA.......................................................................................................................... 3-27 L.E MPLOYER A BATEMENT A SSISTANCE. ........................................................................................................ 3-27 VIII. CLOSING CONFERENCE. .............................................................................. 3-28A.P ARTICIPANTS. ..................................................................................................................................................... 3-28B.D ISCUSSION I TEMS. ............................................................................................................................................ 3-28C.A DVICE TO A TTENDEES .................................................................................................................................... 3-29D.P ENALTIES............................................................................................................................................................. 3-30E.F EASIBLE A DMINISTRATIVE, W ORK P RACTICE AND E NGINEERING C ONTROLS. ............................ 3-30F.R EDUCING E MPLOYEE E XPOSURE. ................................................................................................................ 3-32G.A BATEMENT V ERIFICATION. ........................................................................................................................... 3-32H.E MPLOYEE D ISCRIMINATION .......................................................................................................................... 3-33 IX. SPECIAL INSPECTION PROCEDURES. ...................................................... 3-33A.F OLLOW-UP AND M ONITORING I NSPECTIONS............................................................................................ 3-33B.C ONSTRUCTION I NSPECTIONS ......................................................................................................................... 3-34C. F EDERAL A GENCY I NSPECTIONS. ................................................................................................................. 3-35CHAPTER 4VIOLATIONSI. BASIS OF VIOLATIONS ..................................................................................... 4-1A.S TANDARDS AND R EGULATIONS. .................................................................................................................... 4-1B.E MPLOYEE E XPOSURE. ........................................................................................................................................ 4-3C.R EGULATORY R EQUIREMENTS. ........................................................................................................................ 4-6D.H AZARD C OMMUNICATION. .............................................................................................................................. 4-6E. E MPLOYER/E MPLOYEE R ESPONSIBILITIES ................................................................................................... 4-6 II. SERIOUS VIOLATIONS. .................................................................................... 4-8A.S ECTION 17(K). ......................................................................................................................... 4-8B.E STABLISHING S ERIOUS V IOLATIONS ............................................................................................................ 4-8C. F OUR S TEPS TO BE D OCUMENTED. ................................................................................................................... 4-8 III. GENERAL DUTY REQUIREMENTS ............................................................. 4-14A.E VALUATION OF G ENERAL D UTY R EQUIREMENTS ................................................................................. 4-14B.E LEMENTS OF A G ENERAL D UTY R EQUIREMENT V IOLATION.............................................................. 4-14C. U SE OF THE G ENERAL D UTY C LAUSE ........................................................................................................ 4-23D.L IMITATIONS OF U SE OF THE G ENERAL D UTY C LAUSE. ..............................................................E.C LASSIFICATION OF V IOLATIONS C ITED U NDER THE G ENERAL D UTY C LAUSE. ..................F. P ROCEDURES FOR I MPLEMENTATION OF S ECTION 5(A)(1) E NFORCEMENT ............................ 4-25 4-27 4-27IV.OTHER-THAN-SERIOUS VIOLATIONS ............................................... 4-28 V.WILLFUL VIOLATIONS. ......................................................................... 4-28A.I NTENTIONAL D ISREGARD V IOLATIONS. ..........................................................................................4-28B.P LAIN I NDIFFERENCE V IOLATIONS. ...................................................................................................4-29 VI. CRIMINAL/WILLFUL VIOLATIONS. ................................................... 4-30A.A REA D IRECTOR C OORDINATION ....................................................................................................... 4-31B.C RITERIA FOR I NVESTIGATING P OSSIBLE C RIMINAL/W ILLFUL V IOLATIONS ........................ 4-31C. W ILLFUL V IOLATIONS R ELATED TO A F ATALITY .......................................................................... 4-32 VII. REPEATED VIOLATIONS. ...................................................................... 4-32A.F EDERAL AND S TATE P LAN V IOLATIONS. ........................................................................................4-32B.I DENTICAL S TANDARDS. .......................................................................................................................4-32C.D IFFERENT S TANDARDS. .......................................................................................................................4-33D.O BTAINING I NSPECTION H ISTORY. .....................................................................................................4-33E.T IME L IMITATIONS..................................................................................................................................4-34F.R EPEATED V. F AILURE TO A BATE....................................................................................................... 4-34G. A REA D IRECTOR R ESPONSIBILITIES. .............................................................................. 4-35 VIII. DE MINIMIS CONDITIONS. ................................................................... 4-36A.C RITERIA ................................................................................................................................................... 4-36B.P ROFESSIONAL J UDGMENT. ..................................................................................................................4-37C. A REA D IRECTOR R ESPONSIBILITIES. .............................................................................. 4-37 IX. CITING IN THE ALTERNATIVE ............................................................ 4-37 X. COMBINING AND GROUPING VIOLATIONS. ................................... 4-37A.C OMBINING. ..............................................................................................................................................4-37B.G ROUPING. ................................................................................................................................................4-38C. W HEN N OT TO G ROUP OR C OMBINE. ................................................................................................4-38 XI. HEALTH STANDARD VIOLATIONS ....................................................... 4-39A.C ITATION OF V ENTILATION S TANDARDS ......................................................................................... 4-39B.V IOLATIONS OF THE N OISE S TANDARD. ...........................................................................................4-40 XII. VIOLATIONS OF THE RESPIRATORY PROTECTION STANDARD(§1910.134). ....................................................................................................... XIII. VIOLATIONS OF AIR CONTAMINANT STANDARDS (§1910.1000) ... 4-43 4-43A.R EQUIREMENTS UNDER THE STANDARD: .................................................................................................. 4-43B.C LASSIFICATION OF V IOLATIONS OF A IR C ONTAMINANT S TANDARDS. ......................................... 4-43 XIV. CITING IMPROPER PERSONAL HYGIENE PRACTICES. ................... 4-45A.I NGESTION H AZARDS. .................................................................................................................................... 4-45B.A BSORPTION H AZARDS. ................................................................................................................................ 4-46C.W IPE S AMPLING. ............................................................................................................................................. 4-46D.C ITATION P OLICY ............................................................................................................................................ 4-46 XV. BIOLOGICAL MONITORING. ...................................................................... 4-47CHAPTER 5CASE FILE PREPARATION AND DOCUMENTATIONI.INTRODUCTION ............................................................................................... 5-1 II.INSPECTION CONDUCTED, CITATIONS BEING ISSUED. .................... 5-1A.OSHA-1 ................................................................................................................................... 5-1B.OSHA-1A. ............................................................................................................................... 5-1C. OSHA-1B. ................................................................................................................................ 5-2 III.INSPECTION CONDUCTED BUT NO CITATIONS ISSUED .................... 5-5 IV.NO INSPECTION ............................................................................................... 5-5 V. HEALTH INSPECTIONS. ................................................................................. 5-6A.D OCUMENT P OTENTIAL E XPOSURE. ............................................................................................................... 5-6B.E MPLOYER’S O CCUPATIONAL S AFETY AND H EALTH S YSTEM. ............................................................. 5-6 VI. AFFIRMATIVE DEFENSES............................................................................. 5-8A.B URDEN OF P ROOF. .............................................................................................................................................. 5-8B.E XPLANATIONS. ..................................................................................................................................................... 5-8 VII. INTERVIEW STATEMENTS. ........................................................................ 5-10A.G ENERALLY. ......................................................................................................................................................... 5-10B.CSHO S SHALL OBTAIN WRITTEN STATEMENTS WHEN: .......................................................................... 5-10C.L ANGUAGE AND W ORDING OF S TATEMENT. ............................................................................................. 5-11D.R EFUSAL TO S IGN S TATEMENT ...................................................................................................................... 5-11E.V IDEO AND A UDIOTAPED S TATEMENTS. ..................................................................................................... 5-11F.A DMINISTRATIVE D EPOSITIONS. .............................................................................................5-11 VIII. PAPERWORK AND WRITTEN PROGRAM REQUIREMENTS. .......... 5-12 IX.GUIDELINES FOR CASE FILE DOCUMENTATION FOR USE WITH VIDEOTAPES AND AUDIOTAPES .............................................................. 5-12 X.CASE FILE ACTIVITY DIARY SHEET. ..................................................... 5-12 XI. CITATIONS. ..................................................................................................... 5-12A.S TATUTE OF L IMITATIONS. .............................................................................................................................. 5-13B.I SSUING C ITATIONS. ........................................................................................................................................... 5-13C.A MENDING/W ITHDRAWING C ITATIONS AND N OTIFICATION OF P ENALTIES. .................................. 5-13D.P ROCEDURES FOR A MENDING OR W ITHDRAWING C ITATIONS ............................................................ 5-14 XII. INSPECTION RECORDS. ............................................................................... 5-15A.G ENERALLY. ......................................................................................................................................................... 5-15B.R ELEASE OF I NSPECTION I NFORMATION ..................................................................................................... 5-15C. C LASSIFIED AND T RADE S ECRET I NFORMATION ...................................................................................... 5-16。
斯普林格数学研究生教材丛书
《斯普林格数学研究生教材丛书》（Graduate Texts in Mathematics）GTM001《Introduction to Axiomatic Set Theory》Gaisi Takeuti, Wilson M.Zaring GTM002《Measure and Category》John C.Oxtoby（测度和范畴）（2ed.）GTM003《Topological Vector Spaces》H.H.Schaefer, M.P.Wolff（2ed.）GTM004《A Course in Homological Algebra》P.J.Hilton, U.Stammbach（2ed.）（同调代数教程）GTM005《Categories for the Working Mathematician》Saunders Mac Lane（2ed.）GTM006《Projective Planes》Daniel R.Hughes, Fred C.Piper（投射平面）GTM007《A Course in Arithmetic》Jean-Pierre Serre（数论教程）GTM008《Axiomatic set theory》Gaisi Takeuti, Wilson M.Zaring（2ed.）GTM009《Introduction to Lie Algebras and Representation Theory》James E.Humphreys（李代数和表示论导论）GTM010《A Course in Simple-Homotopy Theory》M.M CohenGTM011《Functions of One Complex VariableⅠ》John B.ConwayGTM012《Advanced Mathematical Analysis》Richard BealsGTM013《Rings and Categories of Modules》Frank W.Anderson, Kent R.Fuller（环和模的范畴）（2ed.）GTM014《Stable Mappings and Their Singularities》Martin Golubitsky, Victor Guillemin （稳定映射及其奇点）GTM015《Lectures in Functional Analysis and Operator Theory》Sterling K.Berberian GTM016《The Structure of Fields》David J.Winter（域结构）GTM017《Random Processes》Murray RosenblattGTM018《Measure Theory》Paul R.Halmos（测度论）GTM019《A Hilbert Space Problem Book》Paul R.Halmos（希尔伯特问题集）GTM020《Fibre Bundles》Dale Husemoller（纤维丛）GTM021《Linear Algebraic Groups》James E.Humphreys（线性代数群）GTM022《An Algebraic Introduction to Mathematical Logic》Donald W.Barnes, John M.MackGTM023《Linear Algebra》Werner H.Greub（线性代数）GTM024《Geometric Functional Analysis and Its Applications》Paul R.HolmesGTM025《Real and Abstract Analysis》Edwin Hewitt, Karl StrombergGTM026《Algebraic Theories》Ernest G.ManesGTM027《General Topology》John L.Kelley（一般拓扑学）GTM028《Commutative Algebra》VolumeⅠOscar Zariski, Pierre Samuel（交换代数）GTM029《Commutative Algebra》VolumeⅡOscar Zariski, Pierre Samuel（交换代数）GTM030《Lectures in Abstract AlgebraⅠ.Basic Concepts》Nathan Jacobson（抽象代数讲义Ⅰ基本概念分册）GTM031《Lectures in Abstract AlgebraⅡ.Linear Algabra》Nathan.Jacobson（抽象代数讲义Ⅱ线性代数分册）GTM032《Lectures in Abstract AlgebraⅢ.Theory of Fields and Galois Theory》Nathan.Jacobson（抽象代数讲义Ⅲ域和伽罗瓦理论）GTM033《Differential Topology》Morris W.Hirsch（微分拓扑）GTM034《Principles of Random Walk》Frank Spitzer（2ed.）（随机游动原理）GTM035《Several Complex Variables and Banach Algebras》Herbert Alexander, John Wermer（多复变和Banach代数）GTM036《Linear Topological Spaces》John L.Kelley, Isaac Namioka（线性拓扑空间）GTM037《Mathematical Logic》J.Donald Monk（数理逻辑）GTM038《Several Complex Variables》H.Grauert, K.FritzsheGTM039《An Invitation to C*-Algebras》William Arveson（C*-代数引论）GTM040《Denumerable Markov Chains》John G.Kemeny, urie Snell, Anthony W.KnappGTM041《Modular Functions and Dirichlet Series in Number Theory》Tom M.Apostol （数论中的模函数和Dirichlet序列）GTM042《Linear Representations of Finite Groups》Jean-Pierre Serre（有限群的线性表示）GTM043《Rings of Continuous Functions》Leonard Gillman, Meyer JerisonGTM044《Elementary Algebraic Geometry》Keith KendigGTM045《Probability TheoryⅠ》M.Loève（概率论Ⅰ）（4ed.）GTM046《Probability TheoryⅡ》M.Loève（概率论Ⅱ）（4ed.）GTM047《Geometric Topology in Dimensions 2 and 3》Edwin E.MoiseGTM048《General Relativity for Mathematicians》Rainer.K.Sachs, H.Wu伍鸿熙（为数学家写的广义相对论）GTM049《Linear Geometry》K.W.Gruenberg, A.J.Weir（2ed.）GTM050《Fermat's Last Theorem》Harold M.EdwardsGTM051《A Course in Differential Geometry》Wilhelm Klingenberg（微分几何教程）GTM052《Algebraic Geometry》Robin Hartshorne（代数几何）GTM053《A Course in Mathematical Logic for Mathematicians》Yu.I.Manin（2ed.）GTM054《Combinatorics with Emphasis on the Theory of Graphs》Jack E.Graver, Mark E.WatkinsGTM055《Introduction to Operator TheoryⅠ》Arlen Brown, Carl PearcyGTM056《Algebraic Topology：An Introduction》W.S.MasseyGTM057《Introduction to Knot Theory》Richard.H.Crowell, Ralph.H.FoxGTM058《p-adic Numbers, p-adic Analysis, and Zeta-Functions》Neal Koblitz（p-adic 数、p-adic分析和Z函数）GTM059《Cyclotomic Fields》Serge LangGTM060《Mathematical Methods of Classical Mechanics》V.I.Arnold（经典力学的数学方法）（2ed.）GTM061《Elements of Homotopy Theory》George W.Whitehead（同论论基础）GTM062《Fundamentals of the Theory of Groups》M.I.Kargapolov, Ju.I.Merzljakov GTM063《Modern Graph Theory》Béla BollobásGTM064《Fourier Series：A Modern Introduction》VolumeⅠ（2ed.）R.E.Edwards（傅里叶级数）GTM065《Differential Analysis on Complex Manifolds》Raymond O.Wells, Jr.（3ed.）GTM066《Introduction to Affine Group Schemes》William C.Waterhouse（仿射群概型引论）GTM067《Local Fields》Jean-Pierre Serre（局部域）GTM069《Cyclotomic FieldsⅠandⅡ》Serge LangGTM070《Singular Homology Theory》William S.MasseyGTM071《Riemann Surfaces》Herschel M.Farkas, Irwin Kra（黎曼曲面）GTM072《Classical Topology and Combinatorial Group Theory》John Stillwell（经典拓扑和组合群论）GTM073《Algebra》Thomas W.Hungerford（代数）GTM074《Multiplicative Number Theory》Harold Davenport（乘法数论）（3ed.）GTM075《Basic Theory of Algebraic Groups and Lie Algebras》G.P.HochschildGTM076《Algebraic Geometry：An Introduction to Birational Geometry of Algebraic Varieties》Shigeru IitakaGTM077《Lectures on the Theory of Algebraic Numbers》Erich HeckeGTM078《A Course in Universal Algebra》Stanley Burris, H.P.Sankappanavar（泛代数教程）GTM079《An Introduction to Ergodic Theory》Peter Walters（遍历性理论引论）GTM080《A Course in_the Theory of Groups》Derek J.S.RobinsonGTM081《Lectures on Riemann Surfaces》Otto ForsterGTM082《Differential Forms in Algebraic Topology》Raoul Bott, Loring W.Tu（代数拓扑中的微分形式）GTM083《Introduction to Cyclotomic Fields》Lawrence C.Washington（割圆域引论）GTM084《A Classical Introduction to Modern Number Theory》Kenneth Ireland, Michael Rosen（现代数论经典引论）GTM085《Fourier Series A Modern Introduction》Volume 1（2ed.）R.E.Edwards GTM086《Introduction to Coding Theory》J.H.van Lint（3ed .）GTM087《Cohomology of Groups》Kenneth S.Brown（上同调群）GTM088《Associative Algebras》Richard S.PierceGTM089《Introduction to Algebraic and Abelian Functions》Serge Lang（代数和交换函数引论）GTM090《An Introduction to Convex Polytopes》Ame BrondstedGTM091《The Geometry of Discrete Groups》Alan F.BeardonGTM092《Sequences and Series in BanachSpaces》Joseph DiestelGTM093《Modern Geometry-Methods and Applications》（PartⅠ.The of geometry Surfaces Transformation Groups and Fields）B.A.Dubrovin, A.T.Fomenko, S.P.Novikov （现代几何学方法和应用）GTM094《Foundations of Differentiable Manifolds and Lie Groups》Frank W.Warner（可微流形和李群基础）GTM095《Probability》A.N.Shiryaev（2ed.）GTM096《A Course in Functional Analysis》John B.Conway（泛函分析教程）GTM097《Introduction to Elliptic Curves and Modular Forms》Neal Koblitz（椭圆曲线和模形式引论）GTM098《Representations of Compact Lie Groups》Theodor Breöcker, Tammo tom DieckGTM099《Finite Reflection Groups》L.C.Grove, C.T.Benson（2ed.）GTM100《Harmonic Analysis on Semigroups》Christensen Berg, Jens Peter Reus Christensen, Paul ResselGTM101《Galois Theory》Harold M.Edwards（伽罗瓦理论）GTM102《Lie Groups, Lie Algebras, and Their Representation》V.S.Varadarajan（李群、李代数及其表示）GTM103《Complex Analysis》Serge LangGTM104《Modern Geometry-Methods and Applications》（PartⅡ.Geometry and Topology of Manifolds）B.A.Dubrovin, A.T.Fomenko, S.P.Novikov（现代几何学方法和应用）GTM105《SL₂ (R)》Serge Lang（SL₂ (R)群）GTM106《The Arithmetic of Elliptic Curves》Joseph H.Silverman（椭圆曲线的算术理论）GTM107《Applications of Lie Groups to Differential Equations》Peter J.Olver（李群在微分方程中的应用）GTM108《Holomorphic Functions and Integral Representations in Several Complex Variables》R.Michael RangeGTM109《Univalent Functions and Teichmueller Spaces》Lehto OlliGTM110《Algebraic Number Theory》Serge Lang（代数数论）GTM111《Elliptic Curves》Dale Husemoeller（椭圆曲线）GTM112《Elliptic Functions》Serge Lang（椭圆函数）GTM113《Brownian Motion and Stochastic Calculus》Ioannis Karatzas, Steven E.Shreve （布朗运动和随机计算）GTM114《A Course in Number Theory and Cryptography》Neal Koblitz（数论和密码学教程）GTM115《Differential Geometry：Manifolds, Curves, and Surfaces》M.Berger, B.Gostiaux GTM116《Measure and Integral》Volume1 John L.Kelley, T.P.SrinivasanGTM117《Algebraic Groups and Class Fields》Jean-Pierre Serre（代数群和类域）GTM118《Analysis Now》Gert K.Pedersen（现代分析）GTM119《An introduction to Algebraic Topology》Jossph J.Rotman（代数拓扑导论）GTM120《Weakly Differentiable Functions》William P.Ziemer（弱可微函数）GTM121《Cyclotomic Fields》Serge LangGTM122《Theory of Complex Functions》Reinhold RemmertGTM123《Numbers》H.-D.Ebbinghaus, H.Hermes, F.Hirzebruch, M.Koecher, K.Mainzer, J.Neukirch, A.Prestel, R.Remmert（2ed.）GTM124《Modern Geometry-Methods and Applications》（PartⅢ.Introduction to Homology Theory）B.A.Dubrovin, A.T.Fomenko, S.P.Novikov（现代几何学方法和应用）GTM125《Complex Variables：An introduction》Garlos A.Berenstein, Roger Gay GTM126《Linear Algebraic Groups》Armand Borel（线性代数群）GTM127《A Basic Course in Algebraic Topology》William S.Massey（代数拓扑基础教程）GTM128《Partial Differential Equations》Jeffrey RauchGTM129《Representation Theory：A First Course》William Fulton, Joe HarrisGTM130《Tensor Geometry》C.T.J.Dodson, T.Poston（张量几何）GTM131《A First Course in Noncommutative Rings》m（非交换环初级教程）GTM132《Iteration of Rational Functions：Complex Analytic Dynamical Systems》AlanF.Beardon（有理函数的迭代：复解析动力系统）GTM133《Algebraic Geometry：A First Course》Joe Harris（代数几何）GTM134《Coding and Information Theory》Steven RomanGTM135《Advanced Linear Algebra》Steven RomanGTM136《Algebra：An Approach via Module Theory》William A.Adkins, Steven H.WeintraubGTM137《Harmonic Function Theory》Sheldon Axler, Paul Bourdon, Wade Ramey（调和函数理论）GTM138《A Course in Computational Algebraic Number Theory》Henri Cohen（计算代数数论教程）GTM139《Topology and Geometry》Glen E.BredonGTM140《Optima and Equilibria：An Introduction to Nonlinear Analysis》Jean-Pierre AubinGTM141《A Computational Approach to Commutative Algebra》Gröbner Bases, Thomas Becker, Volker Weispfenning, Heinz KredelGTM142《Real and Functional Analysis》Serge Lang（3ed.）GTM143《Measure Theory》J.L.DoobGTM144《Noncommutative Algebra》Benson Farb, R.Keith DennisGTM145《Homology Theory：An Introduction to Algebraic Topology》James W.Vick（同调论：代数拓扑简介）GTM146《Computability：A Mathematical Sketchbook》Douglas S.BridgesGTM147《Algebraic K-Theory and Its Applications》Jonathan Rosenberg（代数K理论及其应用）GTM148《An Introduction to the Theory of Groups》Joseph J.Rotman（群论入门）GTM149《Foundations of Hyperbolic Manifolds》John G.Ratcliffe（双曲流形基础）GTM150《Commutative Algebra with a view toward Algebraic Geometry》David EisenbudGTM151《Advanced Topics in the Arithmetic of Elliptic Curves》Joseph H.Silverman（椭圆曲线的算术高级选题）GTM152《Lectures on Polytopes》Günter M.ZieglerGTM153《Algebraic Topology：A First Course》William Fulton（代数拓扑）GTM154《An introduction to Analysis》Arlen Brown, Carl PearcyGTM155《Quantum Groups》Christian Kassel（量子群）GTM156《Classical Descriptive Set Theory》Alexander S.KechrisGTM157《Integration and Probability》Paul MalliavinGTM158《Field theory》Steven Roman（2ed.）GTM159《Functions of One Complex Variable VolⅡ》John B.ConwayGTM160《Differential and Riemannian Manifolds》Serge Lang（微分流形和黎曼流形）GTM161《Polynomials and Polynomial Inequalities》Peter Borwein, Tamás Erdélyi（多项式和多项式不等式）GTM162《Groups and Representations》J.L.Alperin, Rowen B.Bell（群及其表示）GTM163《Permutation Groups》John D.Dixon, Brian Mortime rGTM164《Additive Number Theory：The Classical Bases》Melvyn B.NathansonGTM165《Additive Number Theory：Inverse Problems and the Geometry of Sumsets》Melvyn B.NathansonGTM166《Differential Geometry：Cartan's Generalization of Klein's Erlangen Program》R.W.SharpeGTM167《Field and Galois Theory》Patrick MorandiGTM168《Combinatorial Convexity and Algebraic Geometry》Günter Ewald（组合凸面体和代数几何）GTM169《Matrix Analysis》Rajendra BhatiaGTM170《Sheaf Theory》Glen E.Bredon（2ed.）GTM171《Riemannian Geometry》Peter Petersen（黎曼几何）GTM172《Classical Topics in Complex Function Theory》Reinhold RemmertGTM173《Graph Theory》Reinhard Diestel（图论）（3ed.）GTM174《Foundations of Real and Abstract Analysis》Douglas S.Bridges（实分析和抽象分析基础）GTM175《An Introduction to Knot Theory》W.B.Raymond LickorishGTM176《Riemannian Manifolds：An Introduction to Curvature》John M.LeeGTM177《Analytic Number Theory》Donald J.Newman（解析数论）GTM178《Nonsmooth Analysis and Control Theory》F.H.clarke, Yu.S.Ledyaev, R.J.Stern, P.R.Wolenski（非光滑分析和控制论）GTM179《Banach Algebra Techniques in Operator Theory》Ronald G.Douglas（2ed.）GTM180《A Course on Borel Sets》S.M.Srivastava（Borel 集教程）GTM181《Numerical Analysis》Rainer KressGTM182《Ordinary Differential Equations》Wolfgang WalterGTM183《An introduction to Banach Spaces》Robert E.MegginsonGTM184《Modern Graph Theory》Béla Bollobás（现代图论）GTM185《Using Algebraic Geomety》David A.Cox, John Little, Donal O’Shea（应用代数几何）GTM186《Fourier Analysis on Number Fields》Dinakar Ramakrishnan, Robert J.Valenza GTM187《Moduli of Curves》Joe Harris, Ian Morrison（曲线模）GTM188《Lectures on the Hyperreals：An Introduction to Nonstandard Analysis》Robert GoldblattGTM189《Lectures on Modules and Rings》m（模和环讲义）GTM190《Problems in Algebraic Number Theory》M.Ram Murty, Jody Esmonde（代数数论中的问题）GTM191《Fundamentals of Differential Geometry》Serge Lang（微分几何基础）GTM192《Elements of Functional Analysis》Francis Hirsch, Gilles LacombeGTM193《Advanced Topics in Computational Number Theory》Henri CohenGTM194《One-Parameter Semigroups for Linear Evolution Equations》Klaus-Jochen Engel, Rainer Nagel（线性发展方程的单参数半群）GTM195《Elementary Methods in Number Theory》Melvyn B.Nathanson（数论中的基本方法）GTM196《Basic Homological Algebra》M.Scott OsborneGTM197《The Geometry of Schemes》David Eisenbud, Joe HarrisGTM198《A Course in p-adic Analysis》Alain M.RobertGTM199《Theory of Bergman Spaces》Hakan Hedenmalm, Boris Korenblum, Kehe Zhu（Bergman空间理论）GTM200《An Introduction to Riemann-Finsler Geometry》D.Bao, S.-S.Chern, Z.Shen GTM201《Diophantine Geometry An Introduction》Marc Hindry, Joseph H.Silverman GTM202《Introduction to Topological Manifolds》John M.LeeGTM203《The Symmetric Group》Bruce E.SaganGTM204《Galois Theory》Jean-Pierre EscofierGTM205《Rational Homotopy Theory》Yves Félix, Stephen Halperin, Jean-Claude Thomas（有理同伦论）GTM206《Problems in Analytic Number Theory》M.Ram MurtyGTM207《Algebraic Graph Theory》Chris Godsil, Gordon Royle（代数图论）GTM208《Analysis for Applied Mathematics》Ward CheneyGTM209《A Short Course on Spectral Theory》William Arveson（谱理论简明教程）GTM210《Number Theory in Function Fields》Michael RosenGTM211《Algebra》Serge Lang（代数）GTM212《Lectures on Discrete Geometry》Jiri Matousek（离散几何讲义）GTM213《From Holomorphic Functions to Complex Manifolds》Klaus Fritzsche, Hans Grauert（从正则函数到复流形）GTM214《Partial Differential Equations》Jüergen Jost（偏微分方程）GTM215《Algebraic Functions and Projective Curves》David M.Goldschmidt（代数函数和投影曲线）GTM216《Matrices：Theory and Applications》Denis Serre（矩阵：理论及应用）GTM217《Model Theory An Introduction》David Marker（模型论引论）GTM218《Introduction to Smooth Manifolds》John M.Lee（光滑流形引论）GTM219《The Arithmetic of Hyperbolic 3-Manifolds》Colin Maclachlan, Alan W.Reid GTM220《Smooth Manifolds and Observables》Jet Nestruev（光滑流形和直观）GTM221《Convex Polytopes》Branko GrüenbaumGTM222《Lie Groups, Lie Algebras, and Representations》Brian C.Hall（李群、李代数和表示）GTM223《Fourier Analysis and its Applications》Anders Vretblad（傅立叶分析及其应用）GTM224《Metric Structures in Differential Geometry》Gerard Walschap（微分几何中的度量结构）GTM225《Lie Groups》Daniel Bump（李群）GTM226《Spaces of Holomorphic Functions in the Unit Ball》Kehe Zhu（单位球内的全纯函数空间）GTM227《Combinatorial Commutative Algebra》Ezra Miller, Bernd Sturmfels（组合交换代数）GTM228《A First Course in Modular Forms》Fred Diamond, Jerry Shurman（模形式初级教程）GTM229《The Geometry of Syzygies》David Eisenbud（合冲几何）GTM230《An Introduction to Markov Processes》Daniel W.Stroock（马尔可夫过程引论）GTM231《Combinatorics of Coxeter Groups》Anders Bjröner, Francesco Brenti（Coxeter 群的组合学）GTM232《An Introduction to Number Theory》Graham Everest, Thomas Ward（数论入门）GTM233《Topics in Banach Space Theory》Fenando Albiac, Nigel J.Kalton（Banach空间理论选题）GTM234《Analysis and Probability：Wavelets, Signals, Fractals》Palle E.T.Jorgensen（分析与概率）GTM235《Compact Lie Groups》Mark R.Sepanski（紧致李群）GTM236《Bounded Analytic Functions》John B.Garnett（有界解析函数）GTM237《An Introduction to Operators on the Hardy-Hilbert Space》Rubén A.Martínez-Avendano, Peter Rosenthal（哈代-希尔伯特空间算子引论）GTM238《A Course in Enumeration》Martin Aigner（枚举教程）GTM239《Number Theory：VolumeⅠTools and Diophantine Equations》Henri Cohen GTM240《Number Theory：VolumeⅡAnalytic and Modern Tools》Henri Cohen GTM241《The Arithmetic of Dynamical Systems》Joseph H.SilvermanGTM242《Abstract Algebra》Pierre Antoine Grillet（抽象代数）GTM243《Topological Methods in Group Theory》Ross GeogheganGTM244《Graph Theory》J.A.Bondy, U.S.R.MurtyGTM245《Complex Analysis：In the Spirit of Lipman Bers》Jane P.Gilman, Irwin Kra, Rubi E.RodriguezGTM246《A Course in Commutative Banach Algebras》Eberhard KaniuthGTM247《Braid Groups》Christian Kassel, Vladimir TuraevGTM248《Buildings Theory and Applications》Peter Abramenko, Kenneth S.Brown GTM249《Classical Fourier Analysis》Loukas Grafakos（经典傅里叶分析）GTM250《Modern Fourier Analysis》Loukas Grafakos（现代傅里叶分析）GTM251《The Finite Simple Groups》Robert A.WilsonGTM252《Distributions and Operators》Gerd GrubbGTM253《Elementary Functional Analysis》Barbara D.MacCluerGTM254《Algebraic Function Fields and Codes》Henning StichtenothGTM255《Symmetry Representations and Invariants》Roe Goodman, Nolan R.Wallach GTM256《A Course in Commutative Algebra》Kemper GregorGTM257《Deformation Theory》Robin HartshorneGTM258《Foundation of Optimization》Osman GülerGTM259《Ergodic Theory：with a view towards Number Theory》Manfred Einsiedler, Thomas WardGTM260《Monomial Ideals》Jurgen Herzog, Takayuki HibiGTM261《Probability and Stochastics》Erhan CinlarGTM262《Essentials of Integration Theory for Analysis》Daniel W.StroockGTM263《Analysis on Fock Spaces》Kehe ZhuGTM264《Functional Analysis, Calculus of Variations and Optimal Control》Francis ClarkeGTM265《Unbounded Self-adjoint Operatorson Hilbert Space》Konrad Schmüdgen GTM266《Calculus Without Derivatives》Jean-Paul PenotGTM267《Quantum Theory for Mathematicians》Brian C.HallGTM268《Geometric Analysis of the Bergman Kernel and Metric》Steven G.Krantz GTM269《Locally Convex Spaces》M.Scott Osborne。
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Yan Jurski
A con guration of a timed automaton is given by a control state and nitely many clock (real) values. We show here that the binary reachability relation between con gurations of a timed automaton is de nable in an additive theory of real numbers, which is decidable. This result implies the decidability of model checking for some properties which cannot be expressed in timed temporal logics and provide with alternative proofs of some known decidable properties. Our proof is based on two intermediate results: 1. Every timed automaton can be e ectively emulated by a timed automaton which does not contain nested loops. 2. The binary reachability relation for counter automata without nested loops (called here at automata) is expressible in the additive theory of integers (resp. real numbers). The second result can be derived from 10].
http://www.lsv.ens−cachan.fr/Publis/
Research Report LSV−99−6, Lab. Spécification et Vérification, CNRS & ENS de Cachan, France, July 1999
Short version published in Proc. 10th Int. Conf. Concurrency Theory (CONCUR’99), Eindhoven, NL, Aug. 1999, volume 1664 of Lecture Notes in Computer Science, pages 242−257. Springer, 1999.
Abstract
1 Introduction
Timed automata have been introduced in 4] to model real time systems and became quickly a standard. They roughly consist in adding to nite state automata a nite number of clocks which grow at the same speed. Each transition comes together with some clock resets and an enabling condition, whose satisfaction depends on the current clock values. Temporal properties of real time systems have been expressed and studied through temporal logics such as TPTL 7], TCTL 2, 14, 20], MITL 6], timed -calculi 14, 15]. These logics are in general undecidable, with the notable exception of MITL. On the other hand, the model-checking is decidable for the (real-time) branching time logics, though hard in general. Timed models are harder than untimed ones since they can be seen as in nite state systems in which every con guration consists of a pair of a control state (out of a nite set) and a vector of real clock values. Reasoning about possible clocks values in each state is the core of the di culty. In this paper, we adopt the following point of view: in nite sets of con gurations can be nitely described using constraints. For instance, \(q; x y + z )" is the set of con gurations in control state q and such that the clock x is larger than the sum of clocks y and z . This point of view is not new, as the regions of 2], which are used in a crucial way in the veri cation algorithm, are a representation of sets of con gurations indeed. Here, we go one step further: we express not only sets of con gurations, but also relations between con gurations in a (decidable) constraint system. Then temporal 1
properties of the model are described through the binary reachability relation ? relating ! clock values, which is expressible in the constraint system. Since we may always assume that there is a clock which is never reset by the automaton (and hence is a witness of the total elapsed time), we may express for instance some delay conditions such as \d is a delay between q and q 0 " as a constraint: 9~ ; x0; :(q; ~; ) ? (q 0; x0; + d). Now it is x~ x ! ~ possible to analyse delays between some events such as nding minimal or maximal delays. There are already algorithms which nd such extremal delays 11], but we may also decide properties such as: \the delay between event a and event b is never larger than twice the delay between event a0 and event b0" (which is, up to our knowledge, a new decidability result). More generally, our main result is that the binary reachability relation between clocks values, which is de ned by a timed automaton, is e ectively expressible in the additive theory of real numbers. Since the additive theory of real numbers is decidable, any property which can be expressed in this theory using the reachability relation, can be decided. In particular, we can compute reachable con gurations from a de nable set of con gurations as well as the set of con gurations from which we can reach a de nable set. Hence we have forward and backward model-checking algorithms of safety properties as simple instances of our result. But we may also check properties which express relations between the original and nal clock values. Also, some parametric veri cation is possible as we may keep free variables in the description of original and nal con gurations: for safety properties, the results of 19] can be derived from our main result. On the negative side, not all timed temporal properties can be expressed in the rstorder theory of ? . Typically, unavoidability is not expressible. This is not surprising ! since our logic is decidable, whereas the timed temporal logics are not in general. Our main result is proved in two steps: rst we show that any timed automaton can be emulated by an automaton without nested loops, hereafter called at automaton. The notion of emulation will be precised, but keep only in mind that it preserves the reachability relation. Hence, in some sense, timed automata with a star height n are not more expressive than timed automata with star height 1. (This is not true, of course, if we consider the accepted language instead of the reachability relation as an equivalence on automata). The second step consists of applying one of our former results, which shows that the reachability relation is e ectively expressible in the additive theory of real (resp. integer) numbers for at counter automata 10]. We go from timed automata to automata with counters using an encoding due to L. Fribourg 12]. The emulation result itself is proved in three steps: rst we de ne an equivalence relation on transition sequences, which we show to be a right compatible equivalence of nite index. This is similar to a region construction, though the equivalence is rather on pairs of con gurations than on con gurations. Second, we show some commutation properties of equivalent transition sequences: roughly, equivalent transition sequences can be performed in any order, without a ecting the reachability relation. The third (and last) step consists in using combinatorial arguments on words and proving that there is a at automaton whose language contains a set of representatives for the congruence generated by the commutation properties. (This result can be stated as a formal language property which is independent from the rest of the paper). From this proof, we can also derive some other decidability results. For instance, we can decide whether a sequence of transitions can be iterated. 2