Introduction to the Theory of Computation

出版者:PWS Pub. Co.

作者:Michael Sipser

页数:416

出版时间:1996-12-13

价格:0

装帧:Hardcover

isbn号码:9780534947286

具体描述

This book is aimed as an introductory text book on computer science theory. The book is suited for both undergraduate and graduate studies. The first three chapters of the book, regular expressions, context free languages and the Church-Turing thesis are apt for an introductory class for the undergraduate level. The remaining 7 chapters provide more than enough content for advanced undergraduate or graduate studies.

This is the first book on computer science theory that I have seen, which is actually written in understandable English. As compared to the previous introductory texts by Hopcroft or Papadimitriou, Sipser shuns writting the entire book using just symbols of formal mathematics. This is not to say that there is no formalism in the book. There is adequate use of formal mathematics in the proofs of the book, but not so much as to scare even in most intrepid readers like in previous books on this subject.The fact I liked most about this book is that every proof in the book is accompanied by a "Proof Idea" which explains using diagrams and plain english how exactly the proof works. This followed by the formal proof. The problems at the end of each chapter are fairly interesting, and some of the * marked problems can be fairly challenging for a first time student.

Another amazing thing about this book is the amount of content it covers. I would have never expected a book of only 400 pages to cover computer science theory all the way from introductory undergraduate to advanced graduate levels. This is because, the author focuses only on core concepts and strives to make them as clear as possible. For example, this book has only one chapter on regular expressions, while every other book that I have seen has at least 3-4 chapters full of gory details. This is because Sipser does not go into the gory mechanical details of converting DFAs to NFAs, or writing Turing machines and so on, but instead explains just the important concepts and gives a few examples. Also a wealth of information is to be found in the problems at the end of the chapter. Many of these problems like the Myhill-Nerode theorem are of the kind you will find actually proved in other texts, but left as an exersice here. This is because they are relatively simple to prove once all the concepts are understood. Moreover an educator has the option of which of these problems they want to delve deeper into.

Any student who studies or wishes to study computer science theory should definitely get their hands on this book, irrespective of whether they have already used a different book.

本篇介绍来自amazon.com读者评价

作者简介

Michael Fredric Sipser (born September 17, 1954) is a theoretical computer scientist who has made early contributions to computational complexity theory. He is a professor of Applied Mathematics and Dean of Science at the Massachusetts Institute of Technology.

目录信息

Preface
To the student
To the educator
The current edition
Feedback to the author
Acknowledgments
0 Introduction
0.1 Automata, Computability, and Complexity
0.2 Mathematical Notions and Terminology
0.3 Definitions, Theorems, and Proofs
0.4 Types of Proofs
Part One: Automata and Languages
1 Regular Languages
1.1 Finite Automata
1.2 Nondeterminism
1.3 Regular Expression
1.4 Nonregular Languages
2 Context-Free Languages
2.1 Context-Free Grammar
2.2 Pushdown Automata
2.3 Non-Context-Free Languages
Part Two: Computability Theory
3 The Church-Turing Thesis
3.1 Turing Machines
3.2 Variants of Turing Machines
3.3 The Definition of Algorithm
4 Decidability
4.1 Decidable Languages
4.2 The Halting Problem
5 Reducibility
5.1 Undecidable Problems from Language Theory
5.2 A Simple Undecidable Problem
5.3 Mapping Reducibility
6 Advanced Topics in Computability Theory
6.1 The Recursion Theorem
6.2 Decidability of Logical Theories
6.3 Turing Reducibility
6.4 A Definition of Information
Part Three: Complexity Theory
7 Time Complexity
7.1 Measuring Complexity
7.2 The Class P
7.3 The Class NP
7.4 NP-Completeness
7.5 Additional NP-Complete Problems
8 Space Complexity
8.1 Savitch's Theorem
8.2 The Class PSPACE
8.3 PSPACE-Completeness
8.4 The Classes L and NL
8.5 NL-Completeness
8.6 NL equals coNL
9 Intractability
9.1 Hierarchy Theorems
9.2 Relativization
9.3 Circuit Complexity
10 Advanced Topics in Complexity Theory
10.1 Approximation Algorithms
10.2 Probabilistic Algorithms
10.3 Alternation
10.4 Interactive Proofs Systems
10.5 Parallel Computation
10.6 Cryptography
Selected Bibliography
Index
· · · · · · (收起)

读后感

事知其然而后知其所以然。 现代计算机体系的构建，图灵机的数学模型的实现，正是指出了这道创世纪的光。 现在书里面的内容已经忘记的差不多了，只是记得不断的证明，一步步的证明，充满了智慧的光芒。 总之，是一本好的数学书。  

本书的作者是著名的计算理论方面专家，麻省理工学院应用数学系主任 M. Sipser。全书分为11章，并附有部分习题解答。全书思路清晰，由浅入深，内容详细，是一本零起点学习计算理论的理想教材。我是出于研究需要阅读此书的。其中第零章简要介绍了所需要的基本数学知识。第一到三...

在所有我看过的计算理论、可计算性、计算复杂度的教材中，Sipser的这本Introduction to the Theory of Computation是最适合入门的。把计算理论这么个艰深的学问讲解得清晰简洁，直观易懂。而且涵盖了计算理论的各个经典内容。作为一本introduction，真是再好不过了。 计算理论...  

本书的作者是著名的计算理论方面专家，麻省理工学院应用数学系主任 M. Sipser。全书分为11章，并附有部分习题解答。全书思路清晰，由浅入深，内容详细，是一本零起点学习计算理论的理想教材。我是出于研究需要阅读此书的。其中第零章简要介绍了所需要的基本数学知识。第一到三...

让人了解计算机的本质，它的能力与它的局限性。 计算理论课的教材，上课上的很累，但很有收获。我觉得没读过这本书的不好意思说自己是Computer Science专业毕业的。  

用户评价

关于书中的案例和习题设计，我只能用“匠心独运”来形容。它们并非简单的重复性练习，每一个问题似乎都在精心设计，旨在暴露某个特定理论的细微之处或潜在的陷阱。我花了大量时间在处理某些证明题上，其中一些甚至需要我跳出常规的思维定式，尝试从更宏观的角度去审视问题。特别是那些关于判定性问题和复杂性类别的讨论部分，作者巧妙地引入了一些经典的、具有里程碑意义的研究成果作为例证，让理论不再是空中楼阁，而是深深扎根于计算机科学历史的沃土之中。完成这些挑战性的练习后，我感觉自己的解决问题的能力得到了质的飞跃，这已经超越了学习知识的层面，更像是一场智力上的耐力考验和蜕变过程。

这本书的结构布局堪称教科书级别的典范，其层次分明，脉络清晰，令人印象深刻。从基础的有限状态自动机开始，稳步攀升到图灵机的模型构建，再到不可判定性的深入探讨，整个知识体系的搭建是渐进且无缝连接的。我特别欣赏作者在引入新概念时所采取的策略，总会先回顾前面已经建立的知识基础，确保读者不会在攀爬的过程中迷失方向。对于那些希望系统性掌握该领域知识框架的人来说，这本书提供了一个近乎完美的蓝图。它不仅仅是知识的堆砌，更像是一套精心设计的认知地图，指引读者从最基础的计算单元，一步步走向计算理论的最前沿和最深刻的哲学思考。

坦白说，这本书的深度和广度，让我感觉自己像是站在了一座理论的巨人的肩膀上，获得了俯瞰整个计算疆域的视野。它探讨的问题，关乎“什么可以被计算，什么永远不能被计算”的终极命题，这种宏大的哲学思辨贯穿始终，让人在处理具体的技术细节时，也充满了对计算本质的敬畏感。它不仅仅是一本技术书籍，更像是一份对理性思维的宣言，它教会你如何用最纯粹的逻辑去质疑、去构建、去证明。我从中获得的启发，已经远远超出了课程本身的要求，它塑造了一种看待技术、看待问题、乃至看待世界运行规律的全新底层逻辑框架，其价值是无可估量的。

我必须得说，这本书的语言风格实在是太“克制”了，它仿佛是一位技艺精湛的工匠，用最精确的工具雕刻每一个句子，几乎找不到任何可以被挑剔的冗余词汇。初读时，我感到有些吃力，因为它毫不留情地直击核心概念，没有太多“暖场”的叙述，更别提那些迎合初学者的冗长比喻。这需要读者具备一定的数学基础和专注力，一旦跟上了作者的思维节奏，那种豁然开朗的感觉，是其他任何通俗读物都无法比拟的。它像是一部精密的算法手册，每一条定义和定理都如同不容置疑的公理，严丝合缝，逻辑链条坚不可摧。对于那些追求极致严谨性的读者来说，这本书无疑是一股清流，它挑战你的思维极限，迫使你用最纯粹的逻辑去理解计算的本质边界。

这本书的封面设计简直是一场视觉盛宴，那种深邃的蓝与烫金的字体组合，透露出一种沉稳而又不失深邃的学术气质。我一拿到手，就忍不住被那种厚重感所吸引，仿佛握住的不是一本普通的教科书，而是一份通往理论世界大门的钥匙。内页的纸张质量也是上乘，阅读起来非常舒适，即使长时间沉浸其中，眼睛也不会感到明显的疲劳。更让我惊喜的是，编排的逻辑性极强，每一个章节的过渡都如同行云流水般自然，让人在学习复杂概念时，总能找到清晰的路径。作者在排版上的用心程度，绝对是顶级的，图表的清晰度和准确性，都体现了专业水准，这对于理解那些抽象的计算模型来说，简直是至关重要的加分项。这本书的实体感和设计美学，完全超越了普通教材的范畴，更像是一件值得收藏的艺术品，让人愿意随时翻开它，即使只是静静地欣赏一下那种严谨的美感。

http://www.yinwang.org/blog-cn/2019/07/21/pnp2

酷刑啊。。。读了四章

读过目录

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