# CS代考：计算机科学与工程 Intelligent Science INT201

### Intelligent Science的应用

• 工厂自动化
• 现场和服务机器人
• 辅助机器人
• 军事应用
• 医疗保健
• 教育
• 娱乐
• 视力检查
• 字符识别
• 使用各种生物识别方式（例如面部、指纹、虹膜、手）进行人体识别
• 视觉监控
• 智能交通

• 编程
• 数据结构
• 算法
• 模式识别
• 机器学习
• 人工智能
• 物理
• 数值方法
• 心理学

## 计算机科学与工程 Intelligent Science INT201代考案例

1. Indicate true or false of the following statements and briefly justify your answer.

a) If L is a regular language, then any subset of L is a regular language.

b) If L is a regular language, then L can be accepted by a PDA.

c) Turning machine can accept regular languages, context free languages,

recursive languages.

d) If L1∩L2 is a regular language, then L1 and L2 are regular languages.

e) The regular expressions cab(ab)* and c(aba)*b denotes the same language.

f) The regular expressions c(ab)+ and ca(ba)*b denotes the same language.

2. Let L be a language over {0, 1}, strings of which contain 01 as a substring.

a) Give a regular expression that defines L.

b) Give a NFA by diagram that accepts L.

c) Convert the NFA to an equivalent DFA.

d) Is the DFA obtained by the subset construction in c) a minimum-state DFA? If

yes, justify it. If not, minimise it.

3. a) State the Pumping Lemma and explain how to use it to prove that a language

is not regular.

b) Use the Pumping Lemma to prove the language L = {an bn | n > 0} is not

regular.

c) Show the language L = {an bn | n > 0} is context free by designing a

context–free grammar that generates L.

4. Consider the following ambiguous grammar and answer the questions.

E → a| E + E | E*E

a) What does an ambiguous grammar mean?

b) Give two leftmost derivations of a + a *a. Write down also the associated

derivation trees.

5. Consider the following context free grammar

S → aAS | a| BS | ε

A → SbA | ba

a) Eliminate ε-productions.

b) Eliminate any unit productions in the resulting grammar of a).

c) Eliminate any useless symbols in the resulting grammar of b).

d) Put the resulting grammar in c) into Chomsky normal form.

6. Consider the transition diagram of a Turing machine with doubly infinite tape as below, together with the explanations. The input of this machine is encoded as a unary string x-y, where x and y are sequences of “1”.

In the diagram, state q0 is the initial state and state p is the accepting state. The three-component tuple labelling the transitions stands for the symbol being

scanned, the symbol to be written and the direction of the head move. For

example, at state q0, if the machine is scanning symbol “1”, it will not change the content of the cell being scanned and the head will move one cell to the right. At state q2, if the symbol being scanned is “-” it will be changed to “#” and the head will move one cell to the right. The current state then will change to state p.

For each of the following initial inputs on the tape given below what will be the output?

a) #11111-11#

b) #11-111#

7. a) What are recursive and recursively enumerable languages? Which one of the

two sets stands for decidable problems?

b) What is a reduction? Briefly explain how this technique can be used to prove

that certain problems are undecidable.

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