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计算理论导引(原书第3版)

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计算理论导引(原书第3版)

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《计算理论导引(原书第3版)》由计算理论领域的知名权威MichaelSipser所撰写。他以独特的视角,系统地介绍了计算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。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蕴涵的概念。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。
Catalogue

目录
Introduction to the Theory of Computation,3e
出版者的话
译者序
第3版前言
第2版前言
第1版前言
第0章绪论
0.1自动机、可计算性与复杂性
0.1.1计算复杂性理论
0.1.2可计算性理论
0.1.3自动机理论
0.2数学概念和术语
0.2.1集合
0.2.2序列和多元组
0.2.3函数和关系
0.2.4图
0.2.5字符串和语言
0.2.6布尔逻辑
0.2.7数学名词汇总
0.3定义、定理和证明
0.4证明的类型
0.4.1构造性证明
0.4.2反证法
0.4.3归纳法
练习
问题
习题选解
第一部分自动机与语言
第1章正则语言
1.1有穷自动机
1.1.1有穷自动机的形式化定义
1.1.2有穷自动机举例
1.1.3计算的形式化定义
1.1.4设计有穷自动机
1.1.5正则运算
1.2非确定性
1.2.1非确定型有穷自动机的形式化定义
1.2.2NFA与DFA的等价性
1.2.3在正则运算下的封闭性
1.3正则表达式
1.3.1正则表达式的形式化定义
1.3.2与有穷自动机的等价性
1.4非正则语言
练习
问题
习题选解
第2章上下文无关文法
.......
Introduction

第3版前言Introduction to the Theory of Computation,3e本版新增了关于确定型上下文无关语言的一节。我选择这个主题有以下几个原因。首先,它填补了我之前对自动机理论和语言处理之间的明显空白。以前的版本介绍了有穷自动机以及图灵机在确定型和非确定型上的变形,但却只包含了下推自动机的非确定型变形。因此,增加关于确定型下推自动机的讨论正如同找到完成拼图游戏所缺的那块。
其次,确定型上下文无关文法理论是LR(k)文法的基础,同时也是自动机理论在编程语言和编译器设计上重要且非平凡应用的基础。这个应用将一些关键概念,包括确定型和非确定型有穷自动机的等价性、上下文无关文法和下推自动机之间的相互转换,汇聚一起得到一个高效且漂亮的语法分析方法。这里我们实现了理论和实践的相互联系。
最后,虽然该主题作为自动机理论一个真实的应用非常重要,但它在现有理论教科书中却没有得到足够重视。我研究LR(k)文法多年但一直没有完整理解它们如何工作,也没有看到它们与确定型上下文无关语言理论的完美契合。我写作这一节旨在为理论学者和实践者提供关于这个领域直观而不失严谨的介绍,并由此对该领域做出贡献。需要注意的是:这一节的部分内容非常具有挑战性,因此基础理论课程的教师可考虑将其作为补充读物。之后的章节不依赖于这部分内容。
在撰写本版的过程中,很多人给了我直接或间接的帮助。我很感激两位审阅者Christos Kapoutsis和Cem Say。他们阅读了这一版新内容的初稿,并提供了很有价值的反馈意见。在Cengage Learning的一些人协助了本书的出版工作,特别是Alyssa Pratt和Jennifer FeltriGeorge。Suzanne Huizenga编辑了文字,ByteGraphics的Laura Segel绘制了新的图片并修改了以前版本中的图片。
感谢我在MIT的助教:Victor Chen, Andy Drucker, Michael Forbes, Elena Grigorescu, Brendan Juba, Christos Kapoutsis, Jon Kelner, Swastik Kopparty, Kevin Matulef, Amanda Redlich, Zack Remscrim, Ben Rossman, Shubhangi Saraf, Oren Weimann。他们都给予了我帮助,包括:讨论新的问题并给出解决方法,提出如何让学生理解课程内容的见解。我非常享受与这群有天赋、有热情的年轻人一起工作。
我很高兴收到了来自世界各地的邮件,非常感谢你们的建议、问题和思路。这里有一个相关人员列表,他们的意见对这个版本产生了影响:
Djihed Afifi, Steve Aldrich, Eirik Bakke, Suzanne Balik, Victor Bandur, Paul Beame, Elazar Birnbaum, Goutam Biswas, Rob Bittner, Marina Blanton, Rodney Bliss, Promita Chakraborty, Lewis Collier, Jonathan Deber, Simon Dexter, Matt Diephouse, Peter Dillinger, Peter Drake, Zhidian Du, Peter Fejer, Margaret Fleck, Atsushi Fujioka, Valerio Genovese, Evangelos Georgiadis, Joshua Grochow, Jerry Grossman, Andreas Guelzow, Hjalmtyr Hafsteinsson, Arthur Hall III, Cihat Imamoglu, Chinawat Isradisaikul, Kayla Jacobs, Flemming Jensen, Barbara Kaiser, Matthew Kane, Christos Kapoutsis, Ali Durlov Khan, Edwin Sze Lun Khoo, Yongwook Kim, Akash Kumar, Eleazar Leal, Zsolt Lengvarszky, ChengChung Li, Xiangdong Liang, Vladimir Lifschitz, Ryan Lortie, Jonathan Low, Nancy Lynch, Alexis Maciel, Kevin Matulef, Nelson Max, HansRudolf Metz, Mladen Mika, Sara Miner More, Rajagopal Nagarajan, Marvin Nakayama, Jonas Nyrup, Gregory Roberts, Ryan Romero, Santhosh Samarthyam, Cem Say, Joel Seiferas, John Sieg, Marc Smith, John Steinberger, Nuri Ta?瘙塂demir, Tamir Tassa, Mark Testa, Jesse Tjang, John Trammell, Hiroki Ueda, Jeroen Vaelen, Kurt L. Van Etten, Guillermo Vázquez, Phanisekhar Botlaguduru Venkata, Benjamin BingYi Wang, Lutz Warnke, David Warren, Thomas Watson, Joseph Wilson, David Wittenberg, Brian Wongchaowart, Kishan Yerubandi, Dai Yi。
最重要的是,我要感谢我的家人——我的妻子Ina以及我们的孩子Rachel和Aaron。时光荏苒,岁月如梭,你们的爱就是一切。
Michael Sipser马萨诸塞州,剑桥2012年4月第2版前言Introduction to the Theory of Computation,3e大量读者来的电子邮件反映,第1版没有习题解答是一个缺陷。这一版弥补了这一缺陷。每一章现在都增加了“习题选解”小节,给出了该章的练习和问题中有代表性题目的答案。给出了答案的问题就不能再作为有趣的有挑战性的家庭作业,为弥补这一损失,又添加了若干新问题。教师可以和wwwcoursecom上所指定的相应地区的销售代表联系,索取一份教师手册,其中包含了附加的答案。
第2版的国际版是针对国外读者的。尽管涵盖了同样的主题,它和标准第2版还是有所不同,并且不是用来替代标准第2版的。
许多读者更喜欢学习更多的“标准”主题,比如MyhillNerode定理和Rice定理。通过将这些主题展示在给出答案的问题中,我部分地采纳了这些读者的意见。没有将MyhillNerode定理放到书本主体中是因为我认为,这门课程的目标是初步介绍而非深入研究有穷自动机。有穷自动机在这里的角色是使学生通过研究计算的简单形式模型,为了解复杂模型奠定基础,同时为后续的主题提供方便的例子。当然,一些人希望有更全面的内容,同时另一些人觉得应该略去所有对有穷自动机的引用(或者至少是依赖)。尽管Rice定理对于不可判定性的证明是一个有用的“工具”,第2版还是没有将它放到书本主体中,因为一些学生可能只是机械地使用它而没有真正理解其作用。换用归约来证明不可判定性,可以为学习复杂性理论中出现的归约做更好的准备。
我很感谢我的助教Ilya Baran、Sergi Elizalde、Rui Fan、Jonathan Feldman、Venkatesan Guruswami、Prahladh Harsha、Christos Kapoutsis、Julia Khodor、Adam Klivans、Kevin Matulef、Ioana Popescu、April Rasala、Sofya Raskhodnikova和Iuliu Vasilescu,他们帮助我草拟了若干新问题及其答案。Ching Law、Edmond Kayi Lee和Zulfikar Ramzan也为给出答案付出了努力。感谢Victor Shoup提出了一个简洁的方法,用于修整在第1版中出现在概率原始算法分析中的缺陷。
感谢Course Technology出版社的编辑们的努力,尤其是Alyssa Pratt和Aimee Poirier。多谢Gerald Eisman、Weizhen Mao、Rupak Majumdar、Chris Umans和Christopher Wilson所做的审校。感谢Jerry Moore在编辑上的出色工作,还有ByteGraphics的Laura Segel (lauras@bytegraphicscom) 精彩而又精确的图表再现。
我所收到的电子邮件数量超乎预料。收到来自这么多地方的这么多人的来信绝对是一种快乐。我会尽量回复并向我未曾回复者表示歉意。我在此列出对本书第2版提供了有益的建议的人,同时对所有给我来信的人表示感谢。
Luca Aceto,Arash Afkanpour,Rostom Aghanian,Eric Allender,Karun Bakshi,Brad Ballinger,Ray Bartkus,Louis Barton,Arnold Beckmann,Mihir Bellare,Kevin Trent Bergeson,Matthew Berman,Rajesh Bhatt,Somenath Biswas,Lenore Blum,Mauro ABonatti,Paul Bondin,Nicholas Bone,Ian Bratt,Gene Browder,Doug Burke,Sam Buss,Vladimir Bychkovsky,Bruce Carneal,Soma Chaudhuri,RongJaye Chen,Samir Chopra,Benny Chor,John Clausen,Allison Coates,Anne Condon,Jeffrey Considine,John JCrashell,Claude Crepeau,Shaun Cutts,Susheel MDaswani,Geoff Davis,Scott Dexter,Peter Drake,Jeff Edmonds,Yaakov Eisenberg,Kurtcebe Eroglu,Georg Essl,Alexander TFader,Farzan Fallah,Faith Fich,Joseph EFitzgerald,Perry Fizzano,David Ford,Jeannie Fromer,Kevin Fu,Atsushi Fujioka,Michel Galley,KGanesan,Simson Garfinkel,Travis Gebhardt,Peymann Gohari,Ganesh Gopalakrishnan,Steven Greenberg,Larry Griffith,Jerry Grossman,Rudolf de Haan,Michael Halper,Nick Harvey,Mack Hendricks,Laurie Hiyakumoto,Steve Hockema,Michael Hoehle,Shahadat Hossain,Dave Isecke,Ghaith Issa,Raj DIyer,Christian Jacobi,Thomas Janzen,Mike DJones,Max Kanovitch,Aaron Kaufman,Roger Khazan,Sarfraz Khurshid,Kevin Killourhy,Seungjoo Kim,Victor Kuncak,Kanata Kuroda,Suk YLee,Edward DLegenski,LiWei Lehman,Kong Lei,Zsolt Lengvarszky,Jeffrey Levetin,Baekjun Lim,Karen Livescu,Thomas Lasko,Stephen Louie,TzerHung Low,Wolfgang Maass,Arash Madani,Michael Manapat,Wojciech Marchewka,David MMartin Jr,Anders Martinson,Lyle McGeoch,Alberto Medina,Kurt Mehlhorn,Nihar Mehta,Albert RMeyer,Thomas Minka,Mariya Minkova,Daichi Mizuguchi,GAllen Morris Ⅲ,Damon MoskAoyama,Xiaolong Mou,Paul Muir,German Muller,Donald Nelson,Gabriel Nivasch,Mary Obelnicki,Kazuo Ohta,Thomas MOleson,Jr,Curtis Oliver,Owen Ozier,Rene Peralta,Alexander Perlis,Holger Petersen,Detlef Plump,Robert Prince,David Pritchard,Bina Reed,Nicholas Riley,Ronald Rivest,Robert Robinson,Christi Rockwell,Phil Rogaway,Max Rozenoer,John Rupf,Teodor Rus,Larry Ruzzo,Brian Sanders,Cem Say,Kim Schioett,Joel Seiferas,Joao Carlos Setubal,Geoff Lee Seyon,Mark Skandera,Bob Sloan,Geoff Smith,Marc LSmith,Stephen Smith,Alex CSnoeren,Guy StDenis,Larry Stockmeyer,Radu Stoleru,David Stucki,Hisham MSueyllam,Kenneth Tam,Elizabeth Thompson,Michel Toulouse,Eric Tria,Chittaranjan Tripathy,Dan Trubow,Hiroki Ueda,Giora Unger,Kurt LVan Etten,Jesir Vargas,Bienvenido VelezRivera,Kobus Vos,Alex Vrenios,Sven Waibel,Marc Waldman,Tom Whaley,Anthony Widjaja,Sean Williams,Joseph NWilson,Chris Van Wyk,Guangming Xing,Vee Voon Yee,Cheng Yongxi,Neal Young,Timothy Yuen,Kyle Yung,Jinghua Zhang,Lilla Zollei。
当我夜以继日地坐在我的电脑屏幕前时,尤其要感谢我的家人Ina、Rachel和Aaron的耐心、理解和爱。
Michael Sipser马萨诸塞州,剑桥2004年12月第1版前言Introduction to the Theory of Computation,3e写给学生欢迎使用本书!
将要开始学习的是重要而又引人入胜的课题:计算理论。它包括计算机硬件、软件以及某些应用的基本数学特性。这一课程试图回答什么是不能计算的,什么是能计算的,可以算多快,要用多少存储,以及采用什么计算模型等。这些问题与工程实践有着紧密的联系,也具有纯理论的一面。
许多同学主动盼望学习这门课程,有些同学可能只是为了完成计算机科学或者计算机工程的学位必需的理论课程学分——他们也许认为理论比较神秘、难学且用处不大。
通过学习,读者会发现理论既不神秘、也不讨厌,是好理解、甚至是有趣的。理论计算机科学有许多迷人而重要的思想,同时它也有许多细小的、有时甚至是乏味的细节,这些细节可能令人感到厌倦。学习任何一门新的课程都是一件艰苦的工作。但是,如果能把它适当地表述出来,学习就会变得容易和更愉快些。本书的一个基本目标是让读者接触到计算理论中真正令人激动的方面,而不陷入单调乏味之中。当然,对理论感兴趣的唯一途径是努力去学习并掌握它。
理论与实践是密切联系的,计算理论为实际工作者提供了在计算机工程中使用的理性工具。要为具体的应用设计一个新的程序设计语言吗?本课程中关于语法的内容迟早是会有用的。要进行字符串搜索和模式匹配吗?不要忘了有穷自动机和正则表达式。遇到了一个看来需要比你能够提供的计算机时间还要多的问题吗?想一想你学过的有关NP完全性的内容。各种应用领域,如现代密码协议,都依赖于在这里将要学习的理论原则。
理论是有意义的,它向读者展示了计算机新的、简单的、更加优美的一面,而通常我们把计算机看作一台复杂的机器。最好的计算机设计和应用出自完美的构思。一门理论课程可以提高审美意识,帮助读者建立更加优秀的系统。
理论是实践的指南,学习理论能够扩展你的思维。计算机技术更新很快,专门的技术知识虽然今天有用,但是仅仅在几年内就会变成过时的东西。而能力具有持久的价值,课程应该注重培养思考能力、清楚准确的表达能力、解决问题的能力以及知道问题什么时候还没有解决的能力,理论能够训练这些能力。
除了实际的考虑,几乎每一位使用计算机的人都想了解这个神奇的创造,它的能力,以及它的局限性。为了解答某些基本问题,在过去的30年里,一个全新的数学分支已经确立。这里还有一个重大问题没有解决:如果给定大的自然数,例如有500位,能够在合理的时间内把它分解成素数的乘积吗?即使使用一台超级计算机,现今还没人知道怎样才能在宇宙毁灭之前做完这件事!因子分解问题与现代密码系统中的某些密码有关。去寻找一个快速的因子分解方法吧,也许,读者会因此而一举成名!
写给教师本书是计算机学科高年级本科生或研究生的计算理论入门教材。它涉及计算理论的数学论述,包括叙述和证明定理的基本技能。作者努力使本书适用于那些缺乏定理证明的基本训练的学生,当然,有较多这种经验的学生会学习得更轻松。
强调清楚和生动是本书叙述的一个特色,本课程对某些低层次的细节强调了直觉和“大的轮廓”。例如,虽然在第0章介绍了证明的归纳法以及其他的数学预备知识,但在后面部分它并不是重点。关于自动机的各种构造方法的正确性,一般不用归纳证明。只要叙述清楚,这些构造方法已经是令人信服的,不需进一步论证。归纳证明反而可能把学生搞糊涂而不是给人以启迪。归纳法是比较复杂的技术,可能还有些神秘。对十分明显的事情用归纳法作反复的说明可能会化简为繁、违反初衷,使学生认为数学证明是一种形式化手法,而不是教给他们懂得什么是有说服力的证据,什么不是有说服力的证据。
本书第二部分和第三部分没有采用伪码描述算法,而用了自然语言描述。书中没有花很多时间去设计图灵机(或任何其他形式模型)的程序。现在的学生都有程序设计的经历,觉得丘奇图灵论题是不言自明的。因此我不去用很长的篇幅叙述用一个模型模拟另一个模型来说明它们的等价性。
除增加直观性和压缩某些细节外,本书内容组织符合计算理论中的典型标准。理论工作者将发现,素材的选取、术语以及内容的前后顺序都与其他广泛使用的教材一致。只在少数地方,当我发现标准的术语十分模糊或会引起混淆时,才引进了新的术语。例如,引进名词映射可归约性代替多一可归约性。
习题是学习与数学相关的科学必不可少的环节。书中的习题分成两大类,练习用来复习定义和概念。问题需要多动些脑筋。带星号的问题更难一些。本书努力使练习和问题令人感兴趣,并有挑战性。
反馈给作者互联网为作者与读者之间的交流提供了新的机会。我收到很多电子邮件,对本书的初版提出了建议、赞许和批评,或者指出错误。请继续来函。只要有时间,我尽量亲自给每一个人回信。与本书有关的电子邮箱是sipserbook@mathmitedu另外,还有一个Web站点,包括一张勘误表。可能还有一些其他材料也要加入这个站点用来帮助教师和学生。请告诉我你希望在这里看到什么。这个站点的地址是https://www.math.mit.edu/~sipser/bookhtml致谢如果没有众多朋友、同事以及家人的帮助,我将无法完成这本书。
我要感谢帮助我形成科学观和教育风格的各位老师,其中有五位非常突出。尤其是我的论文指导导师 Manuel Blum,他以独有的方式激励学生,充分展现了他的激情和关怀。他是我和许多人的楷模。感谢Richard Karp将我领入复杂性理论的大门;John Addison为我讲授逻辑并布置了那些精彩的家庭作业;Juris Hartmanis使我了解了计算理论;还有我的父亲,他告诉了我什么是数学、计算机以及教学艺术。


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