形式语言第一章参考答案
语言学教程习题答案第一章
语言学教程习题答案第一章语言学教程习题答案第一章在语言学的学习过程中，习题是非常重要的一部分，通过习题的练习可以帮助我们巩固知识，提高对语言学理论的理解和应用能力。
本文将针对语言学教程第一章的习题进行解答，并对其中一些重要的概念进行深入探讨。
1. 什么是语言学？语言学是研究语言的科学，它涉及到语言的结构、语音、语法、语义、语用等方面的研究。
通过对语言的研究，我们可以了解语言的起源、发展、结构以及语言与思维、文化之间的关系。
2. 语言学的研究方法有哪些？语言学的研究方法包括田野调查、实验研究、文献研究等。
田野调查是指通过对语言使用环境的观察和实地访谈等方式，收集语言数据并进行分析。
实验研究则是通过实验室环境下的控制变量实验，来研究语言现象。
文献研究则是通过对已有的语言学文献进行分析和综述，来推测和总结语言学理论。
3. 语言学的研究对象是什么？语言学的研究对象是语言。
语言是人类交流的工具，它包括语音、词汇、语法等方面的内容。
通过对语言的研究，我们可以了解语言的结构、规律以及语言与思维、文化之间的关系。
4. 什么是语言的层次结构？语言的层次结构是指语言的组成部分之间的关系。
从上到下，语言的层次结构包括语言（language）、语言系统（linguistic system）、语言单位（linguistic unit）以及语言要素（linguistic element）。
语言单位是指语言中的最小有意义的单位，如音素、词素、词等。
语言要素则是指构成语言单位的基本成分，如音素、词素中的音素。
5. 什么是语音学？语音学是研究语言中的语音现象的学科。
它研究的内容包括语音的产生、传播和接收等方面。
通过对语音的研究，我们可以了解语音的分类、规律以及语音与语义、语法之间的关系。
6. 什么是语音？语音是语言中的声音现象。
它是通过声带、口腔、鼻腔等发声器官的协调运动而产生的。
语音可以分为音位和音素两个层次。
音位是语言中的最小音位单位，它是语音的抽象概念。
形式语言 贺利坚_修正版
10
句子
* 定义1-40 句子的并置(concatenation) ：x, y∈∑*, x, y 的并置是由串x直接相接串y所组成的，记作xy。并 置又叫做连结。
* 定义1-40 串x的n次幂 x0=ε xn=xn-1x, n ≥ 1
*例 ∑={a, b} x=aab, y=abaa, xy= aababaa x= ε, y=ab, xy= ab x=aab, x0=ε , x3= aabaabaab
29
文法的形式定义
* 文法示例 G1=({A},{0, 1}, {A→01, A→0A1, A→1A0}, A) G2=({A}, {0,1}, {A→0, A→0A}, A) G3=({A,B},{0,1},{A→01,A→0A1,A→1A0,B→AB, B→0}, A) G4=({A, B},{0, 1},{A→0, A→1, A→0A, A→1A}, A) G5=({S},{0,1},{S→00S, S→11S,S→00, S→11}, S)
31
文法的形式定义
* 约定 ⑴ 对一组有相同左部的产生式 α→β1,α→β2, … ,α→βn 可以简单地记为： α→β1|β2|…|βn 读作：α定义为β1,或者β2 ,…,或者βn 称β1,β2,…，βn为候选式(candidate) 例：S → i|SAS|(S)， A → +|-|*|/
22
基本问题
二、文法的形式定义
* 对任何语言L，有一个字母表∑，使得L⊆∑* * 语言的组成结构是分析、运用语言的基础：
1、语言的描述
$ 一个给定的字符串是否为一个给定语言的句子? $ 如果不是，它在结构的什么地方出了错？ $ 这个错误是什么样的错？如何更正？……。
语言学教程第一章参考答案
Chapter 1 Invitations to Linguistics1. Define the following terms:design feature: the distinctive features of human language that essentially make human language distinguishable from languages of animals.function: the role language plays in communication (e.g. to express ideas, attitudes) or in particular social situations (e.g. religious, legal).synchronic: said of an approach that studies language at a theoretical ¡®point¡¯ in time.diachronic: said of the study of development of language and la nguages over time.prescriptive: to make authoritarian statement about the correctness of a particular use of language.descriptive: to make an objective and systematic account of the patterns and use of a language or variety.arbitrariness: the absence of any physical correspondence between linguistic signals and the entities to which they refer.duality: the structural organization of language into two abstract levels: meaningful units (e.g. words) and meaningless segments (e.g. sounds, letters).displacement: the ability of language to refer to contexts removed from the speaker¡¯s immediate situation.phatic communion: said of talk used to establish atmosphere or maintain social contact.metalanguage: a language used for talking about language.macrolinguistics: a broad conception of linguistic enquiry, including psychological, cultural, etc.competence: unconscious knowledge of the system of grammatical rules in a language.performance: the language actually used by people in speaking or writing.langue: the language system shared by a ¡°speech community¡±.parole: the concrete utterances of a speaker.2. Consult at least four introductory linguistics textbooks (not dictionaries), and copy the definitions of ¡°language¡± that each gives. After carefully comparing the definitions, write a paper discussing which points recur and explaining the significance of the similarities and differences among the definitions.ANSWER:All the definitions should not exclude the description of design features that have been mentioned in this course book. Also it will be better if other design features, say, interchangeability or cultural transmission is included. But it seems impossible to give an unimpeachable definition on language, because the facets people wa nt to emphasize are seldom unanimous. To compare several definitions can make you realize where the argument is.3. Can you think of some words in English which are onomatopoeic? ANSWERS:creak: the sound made by a badly oiled door when it opens.cuckoo: the call of cuckoo.bang: a sudden loud noise.roar: a deep loud continuing sound.buzz: a noise of buzzing.hiss: a hissing sound.neigh: the long and loud cry that a horse makes.mew: the noise that a gull makes.bleat: the sound made by a sheep, goat or calf.4. Do you think that onomatopoeia indicates a non-arbitrary relationship between form and meaning?ANSWER:4. No matter you say "Yes" or "No", you cannot deny that onomatopoeia needs arbitrariness. Before we feel a word is onomatopoeic we should first know which sound the word imitates. Just as what is said in Chapter One, in order to imitate the noise of flying mosquitoes, there are many choices like "murmurous" and "murderous". They both bear more or less resemblance to the genuine natural sound, but "murmurous"is fortunately chosen to mean the noise while "murderous" is chosen to mean something quite different. They are arbitrary as signifiers.5. A story by Robert Louis Stevenson contains the sentence ¡°As the night fell, the wind rose.¡± Could this be expressed as ¡°As the wind rose, the night fell?¡± If not, why? Does this indicate a degree of non-arbitrariness about word order? (Bolinger, 1981: 15)5. Yes. It is a case in point to illustrate non-arbitrariness about word order. When the two parts interchange, the focus and the meaning of the sentence is forced to change, because clauses occurring in linear sequence without time indicators will be taken as matching the actual sequence of happening. The writer¡¯s original intention is distorted, and we can feel it effortlessly by reading. That is why systemic-functionalists and American functionalists think language is not arbitrary at the syntactic level.6. Does the traffic light system have duality? Can you explain by drawinga simple graph?6. Traffic light does not have duality. Obviously, it is not a double-level system. There is only one-to-one relationship between signs and meaning but the meaning units cannot be divided into smaller meaningless elements further. So the traffic light only has the primary level and lacks the secondary level like animals¡¯ calls.ANSWER:Red¡ústopGreen¡úgoYellow¡úget ready to go or stop7. The recursive nature of language provides a theoretical basis for the creativity of language. Can you write a recursive sentence following the example in section 1.3.3.ANSWER:Today I encountered an old friend who was my classmate when I was in elementary school where there was an apple orchard in which we slid to select ripe apples that¡-8. Communication can take many forms, such as sign, speech, body language and facial expression. Do body language and facial expression share or lack the distinctive properties of human language?ANSWER:On a whole, body language and facial expression lack most of the distinctive properties of human language such as duality, displacement, creativity and so on. Body language exhibits arbitrariness a littlebit. For instance, nod means "OK/YES" for us but in Arabian world it is equal to saying "NO". Some facial expressions have non-arbitrariness because they are instinctive such as the cry and laugh of a newborn infant.9. Do you agree with the view that no language is especially simple? ANSWER:Yes. All human languages are complicated systems of communication. It is decided by their shared design features.10. What do you think of Bertrand Russell¡¯s observation of the dog language: ¡°No matter how eloquently a dog may bark, he cannot tell you that his parents were poor but honest¡±? Are you familiar with any type of ways animals communicate among themselves and with human beings? ANSWER:When gazelles sense potential danger, for example, they flee and thereby signal to other gazelles in the vicinity that danger is lurking. A dog signals its wish to be let inside the house by barking and signals the possibility that it might bite momentarily by displaying its fangs.11.Can you mention some typical expressions of phatic communion in Chinese? There is the dialog between Ms. P and Ms. Q. in section 1.5.5. When someone sneezes violently, do you say anything of the nature of phatic communion? Have you noticed your parents or grandparents say something special on such an occasion?Some of the typical phatic expressions in Chinese are: ³ÔÁËÂ𣿠¼ÒÀﶼºÃ°É£¿ÕâÊÇÈ¥ÄÄÀï°¡£¿×î½ü¶¼Í¦ºÃµÄ£¿ANSWER:If someone is sneezing violently, maybe you parents and grandparents may say: ¡°Are you ok?¡±, ¡°Do you need to see a doctor?¡±, ¡°Do you need some water?¡±, ¡°Do you need a handkerchief?¡±, ¡°Do you have a cold?¡± or something like these to show their concerns.12£®There are many expressions in language which are metalingual or self-reflexives, namely, talking about talk and think about thinking, for instance, to be honest, to make a long story short, come to think of it, on second thought, can you collect a few more to make a list of these expressions? When do we use them most often?ANSWER:To tell the truth, frankly speaking, as a matter of fact, to be precise, in other words, that is to saySuch expressions are used most frequently when we want to expatiate the meaning of former clauses in anther way in argumentation.13. Comment on the following prescriptive rules. Do you think they are acceptable?(A) It is I.(B) It is me.You should say A instead of B because ¡°be¡± should be followed by the nominative case, not the accusative according to the rules in Latin.(A) Who did you speak to?(B) Whom did you speak to?You should say B instead of A.(A) I haven't done anything.(B) I haven't done nothing.B is wrong because two negatives make a positive.ANSWER:(1) the Latin rule is not universal. In English, me is informal andI is felt to be very formal.(2) Whom is used in formal speech and in writing; who is more acceptable in informal speech.(3) Language does not have to follow logic reasoning. Here two negative only make a more emphatic negative. This sentence is not acceptable in Standard English not because it is illogical, but because language changes and rejects this usage now.14. The prescriptivism in grammar rules has now shifted to prescriptions in choice of words. In the ¡°guidelines on anti-sexist language¡± issued by the British sociological association, some guidelines are listed below. Do you think they are descriptive and prescriptive? What¡¯s your comment on them?(1) Do not use man to mean humanity in general. Use person, people, human beings, men and women, humanity and humankind.(2) colored: This term is regarded as outdated in the UK and should be avoided as it is generally viewed as offensive to many black peopl e.(3) civilized: This term can still carry racist overtones which derive from a colonialist perception of the world. It is often associated with social Darwinist thought and is full of implicit value judgments and ignorance of the history of the non-industrialized world. ANSWER:They are undoubtedly descriptive. Guidelines are not rules that can determine whether a sentence is right or not. The guidelines advise you to avoid the use of particular words that are grammatically correct but offensive to some certain groups. Actually, they describe the way anti-sexist advocators speak and write.15. Why is the distinction between competence and performance an important one in linguistics? Do you think the line can be neatly drawnbetween them? How do you like the concept ¡°communicative competence¡±? ANSWER:This is proposed by Chomsky in his formalist linguistic theories. It is sometimes hard to draw a strict line. Some researchers in applied linguistics think communicative competence may be a more revealing concept in language teaching than the purely theoretical pair¡ªcompetence and performance.16. Which branch of linguistics do you think will develop rapidly in China and why?It is up to you to decide after you have gone through the whole book. At this stage, we suggest all branches of linguistics have the potential to flourish.17. The following are some well-known ambiguous sentences in syntactic studies of language. Can you disambiguate them?The chicken is too hot to eat.Flying planes can be dangerous.ANSWER:The chicken is too hot to eat.The chicken meat is too hot, so it cannot be eaten at the moment. The chicken feels so hot (maybe after some intense aerobic exercises) that it cannot start eating and needs to calm down first.Flying planes can be dangerous.The ambiguity comes from "flying planes". It can be deciphered as "the planes that is flying" or "to fly planes".18. There are many reasons for the discrepancy between competence and performance in normal language users. Can you think of some of them? ANSWEREthnic background, socioeconomic status, region of the country, and physical state (such as intoxication, fatigue, distraction, illness) vary from individual to individual.19. What do these two quotes reveal about the different emphasis or perspectives of language studies?(1) A human language is a system of remarkable complexity. To come to know a human language would be an extraordinary intellectual achievement for a creature not specifically designed to accomplish this task. A normal child acquires this knowledge on relatively slight exposure and without specific training. He can then quite effortlessly make use of an intricate structure of specific rules and guiding principles to convey his thoughts and feelings to others, ... Thus language is a mirror of mind in a deep and significant sense. It isa product of human intelligence, created anew in each individual by operations that lie far beyond the reach of will or consciousness. (Noam Chomsky: Reflections on Language. 1975: 4)(2) It is fairly obvious that language is used to serve a variety of different needs, but until we examine its grammar there is no clear reason for classifying its uses in any particular way. However, when we examine the meaning potential of language itself, we find that the vast numbers of options embodied in it combine into a very few relatively independent ¡°networks¡±; and these networks of options correspond to certain basic functions of language. This enables us to give an account of the different functions of language that is relevant to the general understanding of linguistic structure rather than to any particular psychological or sociological investigation.(M. A. K. Halliday, 1970: 142)ANSWER:The first quote shows children¡¯s inborn ability of acquiring the knowledge of intricate structure of specific rules. It implies that the language user's underlying knowledge about the system of rules is the valuable object of study for linguists. The second attaches great importance to the functions of language. It regards the use of language as the choice of needed function. The meaning of language can be completely included by a few ¡°networks¡± which is directly related to basic functions of language. It indicates the necessity to study the functions of language.20. You may be familiar with the following proverbs. How do you perceive them according to the arbitrariness and conventionality of language? The proof of the pudding is in the eating.Let sleeping dogs lie.You can¡¯t make a silk purse out of a sow¡¯s ear.Rome was not built in a day.When in Rome, do as the Romans do.All roads lead to Rome.ANSWER:20. Arbitrariness and conventionality derive from the choice of the subject matter. For example, in the ¡°The proof of the puddin g is in the eating.¡± The word ¡°pudding¡± is selected arbitrarily, for we can use another word such as cheese instead of pudding without changing the associative meaning of the proverb. On the other hand, once such links between particular words and associative meaning are fixed, it becomes a matter of conventionality.21. Give examples of situations in which a usage generally considerednon-standard (e.g. ain¡¯t) would be acceptable, even appropriate.ANSWER21. In the talks between intimate friends, one may say ¡°gimme that!¡± instead of ¡°give me that!¡± and ¡°wachya doin¡¯?¡± instead of ¡°what are you doing?¡± and this list may go on.22. The following are some book titles of linguistics. Can you judge the diachronic and diachronic orientation just from the titles? English Examined: Two centuries of Comment on the Mother-Tongue. Protean Shape: A Study in Eighteenth-century Vocabulary and Usage. Pejorative Sense Development in English.The Categories and Types of Present-Day English Word-Formation. Language in the Inner City: Studies in the Black English Vernacular.ANSWER22. Synchronic:Protean Shape: A Study in Eighteenth-century Vocabulary and Usage. The Categories and Types of Present-Day English Word-Formation. Language in the Inner City: Studies in the Black English Vernacular. Diachronic:English Examined: Two centuries of Comment on the Mother-Tongue. Pejorative Sense Development in English。
形式语言参考答案
2．1回答下面的问题： （周期律 02282067） （1）在文法中，终极符号和非终极符号各起什么作用？✓ 终结符号是一个文法所产生的语言中句子的中出现的字符，他决定了一个文法的产生语言中字符的范围。
✓ 非终结符号又叫做一个语法变量，它表示一个语法范畴，文法中每一个产生式的左部至少要还有一个非终结符号，（二，三型文法要求更严，只允许左部为一个非终结符号）他是推导或归约的核心。
（2）文法的语法范畴有什么意义？开始符号所对应的语法范畴有什么特殊意义？ ✓ 文法的非终结符号A 所对应的语法范畴代表着一个集合L （A ），此集合由文法产生式中关于A 的产生式推导实现的✓ 开始符号所对应的语法范畴则为文法G = {V ，T ，P ，S}所产生的语言L （G ）={w S T w w **|⇒∈且}（3）在文法中，除了的变量可以对应一个终极符号行的集合外，按照类似的对应方法，一个字符串也可以对应一个终极符号行集合，这个集合表达什么意义？✓ 字符串对应的终极符号行集合表示这个字符串所能推导到的终极字符串集合，为某个句型的语言。
（4）文法中的归约和推导有什么不同？✓ 推导：文法G = {V ，T ，P ，S}，如果,)(,,* T VP ∈∈→δγβα则称γαδ在G 中推导出了γβδ。
✓ 归约：文法G = {V ，T ，P ，S}，如果,)(,,*T VP ∈∈→δγβα则称γβδ在G 中归约到γαδ。
✓ 这他们的定义，我个人理解两个概念从不同角度看待文法中的产生式，推导是自上而下（从产生式的左边到右边），而归约是自下而上（从产生式的右边到左边），体现到具体实际中，如编译中语法分析时语法树的建立，递归下降，LL （1）等分析法采用自开始符号向下推导识别输入代码生成语法树，对应的LR （1），LALR 等分析法则是采用自输入代码（相当于文法中语言的句子）自底向上归约到开始符号建立语法树，各有优劣。
（5）为什么要求定义语言的字母表上的语言为一个非空有穷集合？ ✓ 非空：根据字母表幂的定义：εε,}{0∑=为字母表中０个字符组成的。
完整版形式语言与自动机课后习题答案部分.ppt
• pp.84：习题 7(1)
用自然语言描述下列文法定义的语言
G: AaaA|aaB
BBcc|D#cc
DbbbD|#
• 解题思路
– 观察每个产生式及其组合产生的子语言的特点； – 根据开始符的产生式将它们并起来就是整个文法产生的语言；
• 解答
(1) D产生式：DbbbD|# – 使用DbbbD可产生句型：(bbb)mD (m1); – 进一步使用D#可得：L(D)={(bbb)m#| m0}
• A|0A|1A；
– 产生语言{0x|x{0, 1}*}的文法
• S0A；
– G: S0A
A|0A|1A
精心整理
11
G FH
课后作业二 (cont.)
• 习题8(3)的解答
– 分析：语言的特点
• {11x11|x*}{111, 11}；
– 产生语言{x|x{0, 1}*}的文法
• A|0A|1A；
– 习题 22 --- 前/后缀
– 习题 23 --- 前/后缀
– 习题 28(1)(2)(10) --- L的描述
精心整理
3
G FH
课后作业一 (cont.)
• pp.40：习题 21
– 判断集合是否字母表的依据
• 非空性
• 有穷性
• 可区分性：字母表中的字符两两互不相同
• 整体性或不可分性
– 解答：(1)、(2) 和(6) 是字母表，其它不是
– 产生子语言{11x11|x*}的文法
• S11A11 ；
– 产生子语言{111, 11}的文法
• S111|11；
– G: S11A11|111|11
A|0A|1A
其它答案 (1) G: S11A|111|11
语言学教程课后习题答案第一章资料(最新整理)
Chapter 1 Invitations to Linguistics1. Define the following terms:design feature: the distinctive features of human language that essentially make human language distinguishable from languages of animals.function: the role language plays in communication (e.g. to express ideas, attitudes) or in particular social situations (e.g. religious, legal).synchronic: said of an approach that studies language at a theoretical ‘point’ in time.diachronic: said of the study of development of language and languages over time. prescriptive: to make authoritarian statement about the correctness of a particular use of language.descriptive: to make an objective and systematic account of the patterns and use of a language or variety.arbitrariness: the absence of any physical correspondence between linguistic signals and the entities to which they refer.duality: the structural organization of language into two abstract levels: meaningful units (e.g. words) and meaningless segments (e.g. sounds, letters).displacement: the ability of language to refer to contexts removed from the speaker’s immediate situation.phatic communion: said of talk used to establish atmosphere or maintain social contact.metalanguage: a language used for talking about language.macrolinguistics: a broad conception of linguistic enquiry, including psychological, cultural, etc.competence: unconscious knowledge of the system of grammatical rules in a language.performance: the language actually used by people in speaking or writing.langue: the language system shared by a “speech community”.parole: the concrete utterances of a speaker.2. Consult at least four introductory linguistics textbooks (not dictionaries), and copy the definitions of “language” that each gives. After carefully comparing the definitions, write a paper discussing which points recur and explaining the significance of the similarities and differences among the definitions.ANSWER:All the definitions should not exclude the description of design features that have been mentioned in this course book. Also it will be better if other design features, say, interchangeability or cultural transmission is included. But it seems impossible to give an unimpeachable definition on language, because the facets people want to emphasize are seldom unanimous. To compare several definitions can make you realize where the argument is.3. Can you think of some words in English which are onomatopoeic?ANSWERS:creak: the sound made by a badly oiled door when it opens.cuckoo: the call of cuckoo.bang: a sudden loud noise.roar: a deep loud continuing sound.buzz: a noise of buzzing.hiss: a hissing sound.neigh: the long and loud cry that a horse makes.mew: the noise that a gull makes.bleat: the sound made by a sheep, goat or calf.4. Do you think that onomatopoeia indicates a non-arbitrary relationship between form and meaning?ANSWER:4. No matter you say "Yes" or "No", you cannot deny that onomatopoeia needs arbitrariness. Before we feel a word is onomatopoeic we should first know which sound the word imitates. Just as what is said in Chapter One, in order to imitate the noise of flying mosquitoes, there are many choices like "murmurous" and "murderous". They both bear more or less resemblance to the genuine natural sound, but "murmurous" is fortunately chosen to mean the noise while "murderous" is chosen to mean something quite different. They are arbitrary as signifiers.5. A story by Robert Louis Stevenson contains the sentence “As the night fell, the wind rose.” Could this be expressed as “As the wind rose, the night fell?” If not, why? Does this indicate a degree of non-arbitrariness about word order? (Bolinger, 1981: 15)5. Yes. It is a case in point to illustrate non-arbitrariness about word order. When the two parts interchange, the focus and the meaning of the sentence is forced to change, because clauses occurring in linear sequence without time indicators will be taken as matching the actual sequence of happening. The writer’s original intention is distorted, and we can feel it effortlessly by reading. That is why systemic-functionalists and American functionalists think language is not arbitrary at the syntactic level.6. Does the traffic light system have duality? Can you explain by drawing a simple graph?6. Traffic light does not have duality. Obviously, it is not a double-level system. There is only one-to-one relationship between signs and meaning but the meaning units cannot be divided into smaller meaningless elements further. So the traffic light only has the primary level and lacks the secondary level like animals’ calls.ANSWER:Red→stopGreen→goYellow→get ready to go or stop7. The recursive nature of language provides a theoretical basis for the creativity of language. Can you write a recursive sentence following the example in section 1.3.3.ANSWER:Today I encountered an old friend who was my classmate when I was in elementary school where there was an apple orchard in which we slid to select ripe apples that…8. Communication can take many forms, such as sign, speech, body language and facial expression. Do body language and facial expression share or lack the distinctive properties of human language?ANSWER:On a whole, body language and facial expression lack most of the distinctive properties of human language such as duality, displacement, creativity and so on. Body language exhibits arbitrariness a little bit. For instance, nod means "OK/YES" for us but in Arabian world it is equal to saying "NO". Some facial expressions have non-arbitrariness because they are instinctive such as the cry and laugh of a newborn infant.9. Do you agree with the view that no language is especially simple?ANSWER:Yes. All human languages are complicated systems of communication. It is decided by their shared design features.10. What do you think of Bertrand Russell’s observation of the dog language: “No matter how eloquently a dog may bark, he cannot tell you that his parents were poor but honest”? Are you familiar with any type of ways animals communicate among themselves and with human beings? ANSWER:When gazelles sense potential danger, for example, they flee and thereby signal to other gazellesin the vicinity that danger is lurking. A dog signals its wish to be let inside the house by barking and signals the possibility that it might bite momentarily by displaying its fangs.11.Can you mention some typical expressions of phatic communion in Chinese? There is the dialog between Ms. P and Ms. Q. in section 1.5.5. When someone sneezes violently, do you say anything of the nature of phatic communion? Have you noticed your parents or grandparents say something special on such an occasion?Some of the typical phatic expressions in Chinese are: 吃了吗？家里都好吧？这是去哪里啊？最近都挺好的？ANSWER:If someone is sneezing violently, maybe you parents and grandparents may say: “Are you ok?”, “Do you need to see a doctor?”, “Do you need some water?”, “Do you need a handkerchief?”, “Do you have a cold?” or something like these to show their concerns.12．There are many expressions in language which are metalingual or self-reflexives, namely, talking about talk and think about thinking, for instance, to be honest, to make a long story short, come to think of it, on second thought, can you collect a few more to make a list of these expressions? When do we use them most often?ANSWER:To tell the truth, frankly speaking, as a matter of fact, to be precise, in other words, that is to saySuch expressions are used most frequently when we want to expatiate the meaning of former clauses in anther way in argumentation.13. Comment on the following prescriptive rules. Do you think they are acceptable?(A) It is I.(B) It is me.You should say A instead of B because “be” should be followed by the nominative case, not the accusative according to the rules in Latin.(A) Who did you speak to?(B) Whom did you speak to?You should say B instead of A.(A) I haven't done anything.(B) I haven't done nothing.B is wrong because two negatives make a positive.ANSWER:(1) the Latin rule is not universal. In English, me is informal and I is felt to be very formal.(2) Whom is used in formal speech and in writing; who is more acceptable in informal speech.(3) Language does not have to follow logic reasoning. Here two negative only make a more emphatic negative. This sentence is not acceptable in Standard English not because it is illogical, but because language changes and rejects this usage now.14. The prescriptivism in grammar rules has now shifted to prescriptions in choice of words. In the “guidelines on anti-sexist language” issued by the British sociological association, someguidelines are listed below. Do you think they are descriptive and prescriptive? What’s your comment on them?(1) Do not use man to mean humanity in general. Use person, people, human beings, men and women, humanity and humankind.(2) colored: This term is regarded as outdated in the UK and should be avoided as it is generally viewed as offensive to many black people.(3) civilized: This term can still carry racist overtones which derive from a colonialist perception of the world. It is often associated with social Darwinist thought and is full of implicit value judgments and ignorance of the history of the non-industrialized world.ANSWER:They are undoubtedly descriptive. Guidelines are not rules that can determine whether a sentence is right or not. The guidelines advise you to avoid the use of particular words that are grammatically correct but offensive to some certain groups. Actually, they describe the way anti-sexist advocators speak and write.15. Why is the distinction between competence and performance an important one in linguistics? Do you think the line can be neatly drawn between them? How do you like the concept “communicative competence”?ANSWER:This is proposed by Chomsky in his formalist linguistic theories. It is sometimes hard to draw a strict line. Some researchers in applied linguistics think communicative competence may be a more revealing concept in language teaching than the purely theoretical pair—competence and performance.16. Which branch of linguistics do you think will develop rapidly in China and why?It is up to you to decide after you have gone through the whole book. At this stage, we suggest all branches of linguistics have the potential to flourish.17. The following are some well-known ambiguous sentences in syntactic studies of language. Can you disambiguate them?The chicken is too hot to eat.Flying planes can be dangerous.ANSWER:The chicken is too hot to eat.The chicken meat is too hot, so it cannot be eaten at the moment.The chicken feels so hot (maybe after some intense aerobic exercises) that it cannot start eating and needs to calm down first.Flying planes can be dangerous.The ambiguity comes from "flying planes". It can be deciphered as "the planes that is flying" or "to fly planes".18. There are many reasons for the discrepancy between competence and performance in normal language users. Can you think of some of them?ANSWEREthnic background, socioeconomic status, region of the country, and physical state (such as intoxication, fatigue, distraction, illness) vary from individual to individual.19. What do these two quotes reveal about the different emphasis or perspectives of language studies?(1) A human language is a system of remarkable complexity. To come to know a human language would be an extraordinary intellectual achievement for a creature not specifically designed to accomplish this task. A normal child acquires this knowledge on relatively slight exposure and without specific training. He can then quite effortlessly make use of an intricate structure of specific rules and guiding principles to convey his thoughts and feelings to others, ... Thus language is a mirror of mind in a deep and significant sense. It is a product of human intelligence, created anew in each individual by operations that lie far beyond the reach of will or consciousness.(Noam Chomsky: Reflections on Language. 1975: 4)(2) It is fairly obvious that language is used to serve a variety of different needs, but until we examine its grammar there is no clear reason for classifying its uses in any particular way. However, when we examine the meaning potential of language itself, we find that the vast numbers of options embodied in it combine into a very few relatively independent “networks”; and these networks of options correspond to certain basic functions of language. This enables us to give an account of the different functions of language that is relevant to the general understanding of linguistic structure rather than to any particular psychological or sociological investigation. (M. A. K. Halliday, 1970: 142)ANSWER:The first quote shows children’s inborn ability of acquiring the knowledge of intricate structure of specific rules. It implies that the language user's underlying knowledge about the system of rules is the valuable object of study for linguists. The second attaches great importance to the functions of language. It regards the use of language as the choice of needed function. The meaning of language can be completely included by a few “networks” which is directly related to basic functions of language. It indicates the necessity to study the functions of language.20. You may be familiar with the following proverbs. How do you perceive them according to the arbitrariness and conventionality of language?The proof of the pudding is in the eating.Let sleeping dogs lie.You can’t make a silk purse out of a sow’s ear.Rome was not built in a day.When in Rome, do as the Romans do.All roads lead to Rome.ANSWER:20. Arbitrariness and conventionality derive from the choice of the subject matter. For example, in the “The proof of the pudding is in the eating.” The word “pudding” is selected arbitrarily, for we can use another word such as cheese instead of pudding without changing the associative meaning of the proverb. On the other hand, once such links between particular words and associativemeaning are fixed, it becomes a matter of conventionality.21. Give examples of situations in which a usage generally considered non-standard (e.g. ain’t) would be acceptable, even appropriate.ANSWER21. In the talks between intimate friends, one may say “gimme that!” instead of “give me that!” and “wachya doin’?” instead of “what are you doing?” and this list may go on.22. The following are some book titles of linguistics. Can you judge the diachronic and diachronic orientation just from the titles?English Examined: Two centuries of Comment on the Mother-Tongue.Protean Shape: A Study in Eighteenth-century Vocabulary and Usage.Pejorative Sense Development in English.The Categories and Types of Present-Day English Word-Formation.Language in the Inner City: Studies in the Black English Vernacular.ANSWER22. Synchronic:Protean Shape: A Study in Eighteenth-century Vocabulary and Usage.The Categories and Types of Present-Day English Word-Formation.Language in the Inner City: Studies in the Black English Vernacular.Diachronic:English Examined: Two centuries of Comment on the Mother-Tongue.Pejorative Sense Development in English。
形式语言与自动机理论--第一章(蒋宗礼)
差(difference)
• 属于A，但不属于B的所有元素组成的集合叫做A 与B的差，记作A-B。
A-B={a|a∈A且aB}
• “-”为减(差)运算符，A-B读作A减B。
• ⑴ A-A=Φ。
⑵ A-Φ=A。 ⑶ A-B ≠ B-A。 ⑷ A-B=A iff A∩B=Φ。 ⑸ A∩(B-C)=(A∩B)-(A∩C)。 ⑹ |A-B|≤|A|。
达式； ⑵ 归纳：如果E1、E2是表达式，则 +E1、-E1、
E1+E2、 E1-E2 、E1*E2 、E1/E2、E1**E2、 Fun(E1)是算术表达式。其中Fun为函数名。 ⑶ 只有满足(1)和(2)的才是算术表达式。
1.2.4 递归定义与归纳证明
立； ⑷ 对任意的i，j，i≠j，Si中的任意元素a和Sj中的任
意元素b，aRb恒不成立
1.2.1 二元关系(binary relation)
• 指数(index)
– 把R将S分成的等价类的个数称为是R在S上的 指数。如果R将S分成有穷多个等价类，则称R 具有有穷指数；如果R将S分成无穷多个等价类， 则称R具有无穷指数。
1.2.1 二元关系(binary relation)
⑴ R1R2≠R2R1。 ⑵ (R1R2)R3=R1(R2R3)。 ⑶ (R1∪R2)R3=R1R3∪R2R3。 ⑷ R3(R1∪R2)=R3R1∪R3R2。 ⑸ (R1∩R2)R3R1R3∩R2R3。 ⑹ R3(R1∩R2)R3R1∩R3R2。
形式语言与自动机理论--第一章 (蒋宗礼)
课程目的和基本要求
• 课程性质
–技术基础
• 基础知识要求
–数学分析（或者高等数学），离散数学
• 主要特点
形式语言与自动机课后习题答案
形式语言与自动机课后习题答案形式语言与自动机课后作业答案第二章4．找到右线性文法，能够形成长度为1至5个字符且以字母领衔的字符串。
请问：g={n,t,p,s}其中n={s,a,b,c,d}t={x,y}其中x∈{所有字母}y∈{所有的字符}p如下:s→xs→xaa→ya→ybb→yb→ycc→yc→ydd→y6．结构上下文毫无关系文法能产生l={ω/ω∈{a,b}*且ω中a的个数是b的两倍}答：g={n,t,p,s}其中n={s}t={a,b}p 如下:s→aabs→abas→baas→aabss→aasbs→asabs→saabs→abass→absas→asbas→sabas→baass→basas→bsaas→sbaa7．找到由以下各组生成式产生的语言（初始每刊s）(1)s→sass→b(2)s→asbs→c(3)s→as→aee→as请问：（1）b(ab)n/n≥0}或者l={(ba)nb/n≥0}(2)l={ancbn/n≥0}(3)l={a2n+1/n≥0}第三章1．下列集合是否为正则集，若是正则集写出其正则式。
（1）所含偶数个a和奇数个b的{a,b}*上的字符串子集（2）所含相同个数a和b的字符串子集（3）不不含子串aba的{a,b}*上的字符串子集请问：（1）就是正则集，自动机如下偶a偶ba奇a偶babbbba偶a奇b奇a奇ba(2)不是正则集，用泵浦定理可以证明，具体内容见到17题（2）。
(3)是正则集先看l’为包含子串aba的{a,b}*上的字符串集合显然这是正则集，可以写出表达式和画出自动机。
（略）则不包含子串aba的{a,b}*上的字符串集合l是l’的非。
根据正则集的性质，l也就是正则集。
4．对下列文法的生成式，找出其正则式（1）g=({s,a,b,c,d},{a,b,c,d},p,s),生成式p如下：s→aas→ba→absa→bbb→bb→ccc→dd→bbd→d（2）g=({s,a,b,c,d},{a,b,c,d},p,s),生成式p如下：s→aas→ba→cca→bbb→bbb→ac→dc→abbd→d请问：(1)由生成式得：s=aa+b①a=abs+bb②b=b+cc③c=d④d=d+bb⑤③④⑤式化简解出cd，获得b=b+c(d+bb)即b=cbb+cd+b=>b=(cb)*(cd+b)⑥将②⑥代入①s=aabs+ab(cb)*(cd+b)+(cb)*(cd+b)=>s=(aab)*(ab+ε)(cb)*(cd+b)(2)由生成式得：s=aa+b①a=bb+cc②b=a+bb③c=d+abb④d=db⑤由③得b=b*a⑥将⑤⑥代入④c=d+abb*a=d+ab+a⑦++将⑥⑦代入②a=ba+c(d+ba)⑧++将⑥⑧代入①s=a(ba+c(d+aba))+b*a=ab+a+acd+acab+a+b*a5.为下列正则集，构造右线性文法：(1){a,b}*(2)以abb结尾的由a和b共同组成的所有字符串的子集(3)以b为首后跟若干个a的字符串的集合(4)所含两个相继a和两个相继b的由a和b共同组成的所有字符串子集请问：（1）右线性文法g=({s},{a,b},p,s)p:s→ass→bss→ε(2)右线性文法g=({s},{a,b},p,s)p:s→ass→bss→abb(3)此正则集为{ba*}右线性文法g=({s,a},{a,b},p,s)p:s→baa→aaa→ε(4)此正则集为{{a,b}*aa{a,b}*bb{a,b}*,{a,b}*bb{a,b}*aa{a,b}*}右线性文法g=({s,a,b,c},{a,b},p,s)p:s→a s/bs/aaa/bbba→aa/ba/bbcb→ab/bb/aacc→ac/bc/ε7.设正则集是a(ba)*(1)结构右线性文法(2)找出（1）中文法的有限自动机请问：（1）右线性文法g=({s,a},{a,b},p,s)p:s→aaa→bsa→ε（2）自动机如下：ap1p2b(p2就是终结状态)9.对应图（a）(b)的状态转换图写出正则式。
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第一章参考答案1.1请用列举法给出下列集合。
（吴贤珺 02282047）⑴ 你知道的各种颜色。
解：{红，橙，黄，绿，青，蓝，紫} ⑵ 大学教师中的各种职称。
解：{助教，讲师，副教授，教授} ⑶ 你所学过的课程。
解：{语文，数学，英语，物理，化学，生物，历史，地理，政治} ⑷ 你的家庭成员。
解：{父亲，母亲，妹妹，我} ⑸ 你知道的所有交通工具。
解：{汽车，火车，飞机，轮船，马车}⑹ 字母表{a , b}上长度小于4的串的集合。
解：{a,b,aa,bb,ab,ba,aaa,aab,aba,abb,baa,bab,bba,bbb} ⑺ 集合{1,2,3,4}的幂集。
解：{Φ,{1},{2},{3},{4},{1,2},{1,3},{1,4},{2,3},{2,4},{3,4},{1,2,3},{1,2,4},{1,3,4},{2,3,4},{1,2,3,4} } ⑻ 所有的非负奇数。
解：{1,3,5,7,…}⑼ 0～100的所有正整数。
解：{1,2,3, (100)(10) 1～10之间的和为10的整数集合的集合。
解：设所求的集合为A ，集合A 中的元素为A i （i=1,2,3,…），A i 也是集合，A i 中的元素在1～10之间，并且和为10。
根据集合元素的彼此可区分性，可以计算出A i 中元素的最多个数，方法是：把1开始的正整数逐个相加，直到等于10（即10=1+2+3+4），这样，A i 中最多有4个元素。
原因是：从最小的1开始，每次加入新的元素都只依次增加1，这样相加的和最小，要加到10，元素个数就最多。
求出最大的∣A i ∣＝4后，再求出元素个数为3，2，1的集合就可以了。
故A={{10},{1,9},{2,8},{3,7},{4,6},{1,2,7},{1,3,6},{1,4,5},{2,3,5},{1,2,3,4}}1.2 请用命题法给出下列集合****2.(1){|0100}(2){|{,}||4}(3){|{1,2,3,4}}(4){|{,}*}(5){|21,}(6){(,)|10,[4,9]}(7){|{01}0}|{01}|{01}x x x z x x a b x B B L L a b x x n n N a b a b a b x x x x x x x x x ≤≤∈∈<⊆⊆=-∈+=∈∈∈∈且且且，，且中的个数是1的个数的两倍（8）{，，且中1的个数是10}(9){，，且中倒数第十个字符|||1,[1,10],[1,||],A i i i i x A x i A x =∀∈∈∈∑为1}（10）{A|=10}1.3 给出下列集合的幂集.（02282075 冯蕊） (1) Φ (2) {Φ} (3) {Φ,{Φ}} (4) {ε,0,00} (5) {0,1} 解答: (1) {Φ}(2) {Φ,{Φ}}(3) {Φ,{Φ},{{Φ}},{Φ,{Φ}}}(4) {Φ,{ε},{0},{00},{ε,0},{ε,00},{0,00},{ε,0,00}} (5) {Φ,{0},{1},{0,1}}1.4.列出集合{0，1，2，3，4}中 (褚颖娜 02282072) （1） 所有基数为3的子集{0，1，2}，{0，1，3}，{0，1，4}，{0，2，3，}，{0，2，4}，.{1，2，3}，{1，2，4}，{1，3，4}，{0，3，4}，{2，3，4}（2） 所有基数不大于3的子集Ф，{0}，{1}，{2}，{3}，{4}，{3，4}，{2，4}，{2，3}，{1，4}，{1，3}，{0，4}，{0，3}，{0，2}，{1，2}，{0，1}，{0，1，2}，{0，1，3}{0，1，4}，{0，2，3，}，{0，2，4}，.{1，2，3}，{1，2，4}，{1，3，4}，{0，3，4}，{2，3，4}1.5解答：1、3、8、10、11、12、16正确1.6证明下列各题目（02282081 刘秋雯）1）A=B，iff A是B的子集且B是A的子集证明：充分条件：∵A=B则由集合相等的定义知对于任何x∈A，有x∈B∴A为B的子集同理，B为A的子集必要条件：∵A为B的子集∴对于任何x∈A，都有x∈B又∵B为A的子集，∴对于任何x∈B有，x∈A由集合相等的定义知，A=B2）如果A为B的子集，则|A|〈=|B|证明：A为B的子集，则对于任何x∈A有x∈B,∴存在一个集合C 使B=A∪C 且A∩C为空集则|B|=|A|+|C||C|〉=0∴|A|〈=|B|3）如果A为B的真子集，则|A|〈=|B|证明：（1）当A为有穷集合时，因为A为B的真子集，且则对于任何x∈A有x∈B,且存在∈B的x，此x不∈A∴存在一个非空集合C ，使B=A∪C 且A∩C为空集则|B|=|A|+|C| 且|C|〉=1∴|A|〈|B|（2）当A为无穷集合，因为A为B的真子集，则B一定也为无穷集合，|A|＝∞，|B|＝∞∴|A|=|B|综合（1），（2）所述，|A|<=|B|4）如果A是有穷集且A为B的真子集则|A|〈|B|证明：见上题证明（1）5）如果A为B的子集，则对于任何x∈A，有x∈B证明：若A为B的子集，则由子集定义可知，对于任何x∈A，有x∈B6）如果A是B的真子集，则对于任何x∈A，有x∈B，并且存在x∈B，但x不∈A 证明：由真子集的定义可证7）如果A为B的子集，B为C的子集，则A为C的子集证明：A为B的子集，B为C的子集则对于任何x∈A，则x都∈B，且，又对于任何y∈B，则y∈C，∴对于任何x∈A，x∈C∴A为C的子集8）如果A为B的真子集，B为C的真子集，则A为C的真子集证明：A为B的真子集，B为C的真子集则对于任何x∈A，则x都∈B，且，存在x∈B但次x不∈A，又对于任何y∈B，则y∈C，存在y∈C但此y不∈B，∴对于任何x∈A，x∈C，存在x∈C.x不∈A∴A为C的真子集9）如果A为B的子集，B为C的真子集，则A为C的真子集证明：因为A为B的子集，B为C的真子集则对于任何x∈A， x都∈B，且x都∈C又对于任何y∈B，则y∈C，存在y∈C但此y不∈B，则y不∈A∴对于任何x∈A，x∈C，存在x∈C.x不∈A∴A为C的真子集10）如果A为B的真子集，B为C的子集，则A为C的真子集证明：A为B的真子集，B为C的子集则对于任何x∈A，则x都∈B，且存在x∈B但次x不∈A，又对于任何y∈B，则y∈C∴对于任何x∈A，x∈C，存在x∈C.x不∈A∴A为C的真子集11）如果A=B，则|A|=|B|证明：A=B，则A与B所含元素相同∴|A|=|B|12）如果A为B的子集，B为C的真子集，或如果A为B的真子集，B为C的子集，则A为C的真子集证明：证明见9，101.7 A = {1,2,3,4,5,6} B = {1,3,5} C = {2,4,6} U = {0,1,2,3,4,5,6,7,8,9}A(1). B= {1,3,5} = B(2). C B A )( = {1,3,5} }6,4,2{ ={1,2,3,4,5,6} = A (3). )()(C U B A -= {1,3,5} }9,8,7,5,3,1,0{ ={0,1,3,5,7,8,9} = C(4).A-B-C= {2,4,6} – {2,4,6} =Φ(5).A × B × C ×Φ =ΦA ×Φ = Φ(6). A C A B A )(= {1,3,5} {0,7,8,9} {0,7,8,9} = {0,1,3,5,7,8,9} = C(7). C A B A ⨯⨯ =C B A ⨯⨯=)},(),(),(|),{(C b B a C b B a C b B a b a A ∈∈∈∈∈∈⨯或或=)},,(),,(),,(|),,{(C c B b A a C c B b A a C c B b A a c b a ∈∈∈∈∈∈∈∈∈或或 (8). C B A B A )( = C A A = C A= A={1，2，3，4，5，6}1．8 对论域U上的集合A、B、C，证明以下结论成立。
（02282047 吴贤珺）⑴ A∪B＝B∪A证：对任意的x，x∈A∪B⇔x∈A∨x∈B⇔x∈B∨x∈A⇔x∈B∪A故A∪B⊆B∪A 且 B∪A⊆A∪B则 A∪B＝B∪A。
⑵ (A∪B)∪C＝A∪(B∪C)证：对任意的x，x∈(A∪B)∪C⇔x∈(A∪B)∨x∈C⇔(x∈A∨x∈B)∨x∈C⇔x∈A∨x∈B∨x∈C⇔x∈A∨(x∈B∨x∈C)⇔x∈A∨x∈(B∪C )⇔x∈A∪(B∪C)故(A∪B)∪C ⊆ A∪(B∪C) 且 A∪(B∪C) ⊆ (A∪B)∪C则 (A∪B)∪C＝A∪(B∪C)。
⑶ A∪B＝A iff B⊆A证：①由B⊆A∪B及 A∪B＝A知 B⊆A。
②由B⊆A 知∀x∈B, x∈A则对任意的x，x∈A∪B⇒x∈A∨x∈B⇒x∈A故 A∪B⊆A，又A⊆A∪B，所以 A∪B＝A。
综合①②得到 A∪B＝A iff B⊆A。
⑷ A×(B∪C)＝(A×B)∪(A∪C)证：对任意的有序对(a, b)，(a, b)∈A×(B∪C)⇔a∈A∧b∈(B∪C)⇔a∈A∧(b∈B∨b∈C)⇔(a∈A∧b∈B)∨( a∈A∧b∈C)⇔(a, b)∈A×B∨(a, b)∈A×C⇔(a, b)∈(A×B)∪(A×C)故A×(B∪C) ⊆ (A×B)∪(A∪C) 且 (A×B)∪(A∪C) ⊆ A×(B∪C)则 A×(B∪C)＝(A×B)∪(A∪C)。
⑸ (B∩C)×A＝(B×A)∩(C×A)证：对任意的有序对(b, a)，(b, a)∈(B∩C)×A⇔b∈(B∩C)∧a∈A⇔(b∈B∧b∈C)∧a∈A⇔(b∈B∧a∈A)∧(b∈C∧a∈A)⇔(b, a)∈B×A∧(b, a)∈C×A⇔(b, a)∈(B×A)∩(C×A)故(B∩C)×A ⊆ (B×A)∩(C×A) 且 (B×A)∩(C×A) ⊆ (B∩C)×A则 (B∩C)×A＝(B×A)∩(C×A)。
⑹ A×(B－C)＝(A×B)－(A×C)证：对任意的有序对(a, b)，(a, b)∈A×(B－C)⇔a∈A∧b∈(B－C)⇔a∈A∧(b∈B∧b∉C)⇔(a∈A∧b∈B)∧( a∈A∧b∉C)⇔(a, b)∈A×B∧(a, b)∉A×C⇔(a, b)∈(A×B)－(A×C)故A×(B∪C) ⊆ (A×B)∪(A∪C) 且 (A×B)∪(A∪C) ⊆ A×(B∪C)则 A×(B∪C)＝(A×B)∪(A∪C)。