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本书由计算机理论领域的知名权威Michaael Sipser所撰写。他以独特的视角，系统地介绍了计算机理论的三个主要内容：自动机与语言、可计算性理论和计算复杂性理论。约大部分内容是基本的，同时对可计算性和计算复杂性理论中的某些高级内容进行了重点介绍。作者以清新的笔触、生动的语言给出了宽泛的数学原理，而没有拘泥于某些低层次的细节。在证明之前，均有“证明思路”，帮助读者理解数学形式下涵的概念。同样，对于算法描述，均以直观的文字而非伪代码给出，从而将注意力集中于算法本身，而不是某些模型。新版根据多年来使用本书的教师和学生的建议进行了改进，并对课堂测试题进行了全面的更新，每章末均有样例解答。

本书可作为计算机专业高年级本科生和研究生的教材，也可作为教师和研究人员的参考书。

Preface to the First Edition

To the student

To the educator

The first edition

Feedback to the author

Acknowledgments

Preface to the Sceond Edition（International）

0 Introduction

0.1 Automata,CompUTABILITY,and Complexity

Complexity theory

Computability theory

0.2 Mathematical Notions and Terminology

Sets

Sequemces and tuples

Functions and relations

Graphs

Strings and languges

Boolean logic

Summary of mathematical terms

0.3 Definitions,Theorems,and Proofs

Finding proofs

0.4 Types of Proof

Proof by construction

Proof by construction

Proof by induction

Exercises,Problims,and Solutions

Part One:Automata and Languages

1 Regular Languages

1.1 Finite Automata

Formal definition of afinite automaton

Examples of finite automata

Formal definition of computation

Designign finite automata

The regular operations

1.2 Nondeteriminism

Formal definition of a nondeterministic finite automaton

Equivalence of NFAs and DFAs

Closure under the regular operations

1.3 Regular Expressions

Formal definition of a regular expression

Equivalence with finite automata

1.4 Nonregular Languages

The pumping lemma for regulan languages

Exercises,Problems,and Solutions

2 Context-Free Languages

2.1 Conetxt-free Grammars

Formal definition of a context-free grammar

Examples of context-free grammars

Designing context-free grammars

Ambiguity

Chomaky mormal form

2.2 Pushdown Automata

Formal definition of a pushdown automaton

Examples of pushdown autonata

Equivalence wish context-free grammars

2.3 Non-context-free Languages

The pumping lemma for context-free languages

Exercises,Problems,and Solutions

Part Two:Computability Theory

Part Three:Computability Theory

Selected Bibliography

Index

Michaael Sipser：麻省理工学院应用数学系教授，计算机科学和人工智能实验室（CSAIL）成员。他从事理论计算机科学与其他数学课程的教学工作25年，目前为数学系主任。他痴迷于复杂性理论，喜欢复杂性理论的教学工作。

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Ignoring the trees to see the forest doesn't mean that one is more important than the other--it just gives a different perspective.

We have come to a turning point in the study of the theory of computation. We continue to speak of Turing machines, but our real focus from now on is on algorithms. That is, the Turing machine merely serves as a precise model for the definition of algorithm. We skip over the extensive theory of Turing machines themselves and do not spend much time on the low-level programming of Turing machines. We need only to be comfortable enough with Turing machines to believe that they capture all algorithms.

Similar to a finite automaton but with an unlimited and unrestricted memory, a Turing machine is a much more accurate model of a general purpose computer. A Turing machine can do everything that a real computer can do. Nonetheless, even a Turing machine cannot solve certain problems. In a very real sense, these problems are beyond the theoretical limits of computation.

书籍介绍

本书由计算机理论领域的知名权威Michaael Sipser所撰写。他以独特的视角，系统地介绍了计算机理论的三个主要内容：自动机与语言、可计算性理论和计算复杂性理论。约大部分内容是基本的，同时对可计算性和计算复杂性理论中的某些高级内容进行了重点介绍。作者以清新的笔触、生动的语言给出了宽泛的数学原理，而没有拘泥于某些低层次的细节。在证明之前，均有“证明思路”，帮助读者理解数学形式下涵的概念。同样，对于算法描述，均以直观的文字而非伪代码给出，从而将注意力集中于算法本身，而不是某些模型。新版根据多年来使用本书的教师和学生的建议进行了改进，并对课堂测试题进行了全面的更新，每章末均有样例解答。

本书可作为计算机专业高年级本科生和研究生的教材，也可作为教师和研究人员的参考书。