内容提要 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。 目录 Preface to the First Edition To the student To the educator The first edition Feedback to the author AcknowledgmentsPreface 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 SolutionsPart 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 SolutionsPart Two:Computability TheoryPart Three:Computability TheorySelected BibliographyIndex 作者介绍 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。 序言
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