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语言与机器:计算机科学理论的导论(原书第3版)

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《语言与机器:计算机科学理论的导论(原书第3版)》不仅介绍了计算机科学的基础,探讨了算法计算的能力和局限;而且还通过概念的严格表述,以及使用通俗的例子来解释定理,从而帮助学生提高数学论证能力。书中每章后面都有一些练习,通过这些练习使学生加深对本章内容的理解。
Content Description

《语言与机器:计算机科学理论的导论(原书第3版)》是计算理论方面的优秀教材之一,包括上下文无关文法、上下文无关文法范式、有限自动机、正则语言的性质、下推自动机和上下文无关语言、图灵机、图灵可计算函数、乔姆斯基层次、判定问题与丘奇图灵机、不可判定性、Mu-递归函数、时间复杂性、库克定理、NP-完全问题、LL(k)文法以及LR(k)文法等问题。《语言与机器:计算机科学理论的导论(原书第3版)》不仅介绍了计算机科学的基础,而且通过概念的严格表述,以及使用通俗的例子来阐释定理,从而帮助学生提高数学论证能力以及对计算理论知识的全面深入的理解。书中每章后面都有附有大量习题,通过完成这些习题,学生可以加深对本章内容的理解。
《语言与机器:计算机科学理论的导论(原书第3版)》可以用作计算机科学、计算机工程及其相关专业的教材,也可以作为从事计算理论、形式语言以及计算机系统研发的研究人员和工程技术人员的参考书。
理论计算机科学是推动计算机技术和应用向前发展的巨大动力。形式语言、自动机、可计算性、计算复杂性和相关方面内容构成的计算理论,是理论计算机科学的基础内容之一。《语言与机器:计算机科学理论的导论(原书第3版)》由美国莱特州立大学计算机科学及工程系的Thomas A.Sudkamp教授编写,是介绍这些内容的优秀教材。
全书不仅介绍了计算机科学的基础,探讨了算法计算的能力和局限;而且还通过概念的严格表述,以及使用通俗的例子来解释定理,从而帮助学生提高数学论证能力。书中每章后面都有一些练习,通过这些练习使学生加深对本章内容的理解。
Author Description

Thomas A.Sudkamp是美国莱特州立大学计算机科学及工程系的教授,他的研究领域
广泛,包括近似推理、人工智能、数理逻辑、建模软计算的应用、复杂问题领域的决策制定以及不确定、不精确信息和知识发掘的机器学习。Sudkamp教授目前还担任IEEE Transactions on System,Man,and Cybemetics和IEEE Transactions on Fuzzy Systems的副编辑,International Journal of Approximate Reasonin9和Fuzzy Sets and Systems的领域编辑。他也曾经担任过北美模糊信息处理协会NAFIPS)的主席以及国际模糊系统联盟(IFSA)的副主席。
Catalogue

出版者的话
专家指导委员会
译者序
前言
绪论
第一部分 基础
第1章 数学预备知识
1.1集合论
1.2笛卡儿积、关系和函数
1.3等价关系
1.4可数集合和不可数集合
1.5对角化和自反
1.6递归定义
1.7数学归纳
1.8有向图
1.9练习
参考文献注释

第2章 语言
2.1字符串和语言
2.2语言的有穷规格说明
2.3正则集合和表达式
2.4正则表达式和文本搜索
2.5练习
参考文献注释

第二部分 文法、自动机和语言
第3章 上下文无关文法
3.1上下文无关文法和语言
3.2文法和语言的例子
3.3正则文法
3.4验证文法
3.5最左推导和二义性
3.6上下文无关文法和编程语言定义
3.7练习
参考文献注释

第4章 上下文无关文法范式
4.1文法转换
4.2消去入规则
4.3去掉链规则
4.4无用符
4.5乔姆斯基范式
4.6CYK算法
4.7去掉直接左递归
4.8格立巴赫范式
4.9练习
参考文献注释

第5章 有限自动机
5.1 一个有限状态自动机
5.2 确定型有限自动机
5.3 状态图和例子
5.4 非确定型有限自动机
5.5 转换
5.6 去掉非确定性
5.7 DFA的最小化
5.8 练习
参考文献注释

第6章 正则语言的性质
6.1 有限状态机接收正则语言
6.2 表达式图
6.3 正则文法和有限自动机
6.4 正则语言的封闭性质
6.5 非正则语言
6.6 规则语言的泵引理
6.7 Myhill-Nerode定理
6.8 练习
参考文献注释

第7章 下推自动机和上下文无关语言
7.1 下推自动机
7.2 PDA的变种
7.3 上下文无关语言的接收
7.4 上下文无关语言的泵引理
7.5 上下文无关语言的封闭性
7.6练习
参考文献注释

第三部分 可计算性
第8章 图灵机
8.1标准图灵机
8.2作为语言接收器的图灵机
8.3可供选择接收标准
8.4多道图灵机
8.5双向图灵机
8.6多带图灵机
8.7非确定型图灵机
8.8用来枚举语言的图灵机
8.9练习
参考文献注释

第9章 图灵可计算函数
9.1函数的计算
9.2数值计算
9.3图灵机的顺序操作
9.4函数的合成
9.5不可计算函数
9.6关于编程语言
9.7练习
参考文献注释

第10章 乔姆斯基层次
10.1无限制文法
10.2上下文有关文法
10.3线性有界自动机
10.4乔姆斯基层次
10.5练习
参考文献注释

第11章 判定问题与丘奇-图灵论题
11.1判定问题的描述
11.2判定问题和递归语言
11.3问题归约
11.4丘奇-图灵论题
11.5通用机
11.6练习
参考文献注释

第12章 不可判定性
12.1图灵机的停机问题
12.2问题归约和不可判定性
12.3其他的停机问题
12.4莱斯定理
12.5不可解决的词问题
12.6波斯特对应问题
12.7上下文无关文法中的不可判定问题
12.8练习
参考文献注释

第13章 Mu-递归函数
13.1原始递归函数
13.2一些原始递归函数
13.3有界操作符
13.4除法函数
13.5歌德尔数字和串值递归
13.6可计算部分函数
13.7 图灵可计算函数和Mu-递归函数
13.8修订的丘奇-图灵论题
13.9练习
参考文献注释

第四部分计算复杂性
第14章 时间复杂性
14.1复杂性度量
14.2增长的速度
14.3图灵机的时问复杂性
14.4复杂性和图灵机的变种
14.5线性加速
14.6语言时间复杂性的属性
14.7计算机计算的模拟
14.8练习
参考文献注释

第15章 P、NP和库克定理
15.1 非确定型图灵机的时间复杂性
15.2P类和NP类
15.3问题表示和复杂性
15.4判定问题和复杂性类
15.5哈密尔顿回路问题
15.6多项式时间归约
15.7 P=NP?
15.8 可满足性问题
15.9 复杂类的关系
15.10练习
参考文献注释

第16章 NP-完全问题
16.1归约和NP-完全问题
16.2三元可满足性问题
16.3三元可满足性的归约
16.4归约和子问题
16.5最优化问题
16.6近似算法
16.7近似方案
16.8练习
参考文献注释

第17章 其他复杂性类
17.1 派生的复杂性类
17.2 空间复杂性
17.3 空间复杂性和时间复杂性的关系
17.4 P-空间,NP-空间和萨维奇定理
17.5 P-空间完全性
17.6 一个难解问题
17.7 练习
参考文献注释

第五部分确定型语法分析
第18章语法分析引论
18.1 文法图
18.2自顶向下语法分析
18.3归约和自底向上语法分析
18.4自底向上语法分析器
18.5语法分析和编译
18.6练习
参考文献注释

第19章LL(k)文法
19.1 上下文无关文法中的预读
19.2 FIRST集合、FOLLOW集合和预读集合
19.3 强LL(k)语法
19.4 FIRSTk集合的构造
19.5 FOLLOWk集合的构造
19.6 强LL(1)文法
19.7 强LL(k)分析器
19.8 LL(k)文法
19.9 练习
参考文献注释

第20章 LR(k)文法
20.1 LR(0)上下文
20.2 LR(0)分析器
20.3 LR(0)机
20.4 被LR(0)机接收
20.5 LR(1)文法
20.6 练习
参考文献注释
附录Ⅰ 标记索引
附录Ⅱ 希腊字母表
附录Ⅲ ASC Ⅱ字符集
附录Ⅲ Java的BNF范式定义
参考文献
索引
Book Abstract

第1章 数学预备知识
集合论和离散数学为形式语言理论、可计算性理论和计算复杂性分析提供了数学基础。我们首先回顾集合论的表示和基本操作。集合的基数度量集合的大小,并提供无穷集合大小的准确定义。德国数学家George Cantor深入研究集合的属性后得出一条有趣的结论,就是存在不同大小的无穷集。尽管Cantor的工作仅仅表明存在一个完整的无穷集合规模层次,但是这已经足够支持我们把无穷集合分成两类的目的了。这两类分别是可数的和不可数的。如果集合的元素数目与自然数一样多,那么这个集合是可数的无穷集。如果元素数目比自然数多,就是不可数无穷集。 .
在本章中,我们将使用对角化论证(diagonalization argument)结构来证明定义在自然数集合上的函数集合是不可数无穷集。我们在有效过程(effective procedure)和可计算函数(computable func—tion)的意义上达成共识后(这也是本书第三部分的主要目的),将能够确定可以用算法计算的函数集合的大小。通过比较这两个集合的大小,就可以证明存在这样的函数,它们的值不能使用任何算法过程计算得到。
一个集合可能由任意一组对象组成,我们对那些机械化生成元素的集合感兴趣。然后,我们介绍可以产生集合元素的递归定义;接着构造递归生成的集合与数学归纳法之间的关系。归纳已经被证明能够为递归产生的无穷集合中的元素性质提供一个通用的证明技巧。
在本章的最后,我们将复习有向图和树等知识,这是贯穿本书的两种结构,并以图形方式的解释了形式语言理论和计算理论的概念。 ……

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Jingdong book