An Introduction to Theory of Computation: An Algorithmic Approach
暫譯: 計算理論導論：算法方法

Ogihara, Mitsunori

An Introduction to Theory of Computation: An Algorithmic Approach
  • 出版商: Springer
  • 出版日期: 2026-04-09
  • 售價: $2,860
  • 貴賓價: 9.5 折 $2,717
  • 語言: 英文
  • 頁數: 382
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031847423
  • ISBN-13: 9783031847424
  • 相關分類: Algorithms-data-structures

    • 海外代購書籍(需單獨結帳)

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商品描述

This textbook aims to provide a comprehensive introduction to the theory of computation for upper-level undergraduate students and first-year graduate students in computer science and related disciplines. It covers a wide range of foundational topics essential for understanding the principles and applications of computation.

The book begins with regular languages, exploring finite automata, nondeterministic finite automata, regular expressions, and the equivalence among these apparatuses. It explores state minimization and the Myhill-Nerode Theorem, offering techniques such as pumping lemmas to identify non-regular languages and using the Myhill-Nerode Theorem for non-regularity proofs. Additionally, the closure properties of regular languages are examined.

Context-free languages are another focal point, where the text discusses context-free grammars, Chomsky normal form grammars, pushdown automata, and their equivalences. The book includes pumping lemmas and closure properties using CNF grammars and PDA analysis, as well as identifying non-context-free languages and understanding leftmost derivations.

Turing machine models are thoroughly covered, with various models and simulations explained. The book outlines configurations, the Church-Turing Thesis, and differentiates between recursive and recursively enumerable languages.

Decidability and undecidability are critical topics in the text, addressing decidable problems, diagonalization, the halting problem, and Rice's Theorem. It also provides a characterization of decidability, discusses the Post Correspondence Problem, and examines the lower levels of the arithmetical hierarchy.

The textbook also delves into computational complexity classes, defining time and space complexity classes, and presenting efficient simulations and hierarchy theorems, including the Hennie-Stearns Theorem. It includes examples of problems in P and NP, providing a clear understanding of these classifications.

NP-completeness is explored in detail, covering SAT and 3SAT, canonical complete problems, and various NP-complete problems. The book extends to space complexity classes, discussing PSPACE complete problems, NL-complete problems, and proving that NL=coNL.

Finally, the text ventures beyond NP-completeness, discussing Ladner's construction of non-NPC sets, randomized complexity classes, and concepts such as BPP and the polynomial hierarchy. It also examines polynomial size circuits, providing a comprehensive view of the landscape of computational complexity.

商品描述(中文翻譯)

這本教科書旨在為高年級本科生和計算機科學及相關學科的一年級研究生提供計算理論的全面介紹。它涵蓋了理解計算原則和應用所需的各種基礎主題。

本書首先介紹正規語言，探討有限自動機、非確定性有限自動機、正規表達式及這些工具之間的等價性。它探討狀態最小化和Myhill-Nerode定理，提供如抽泣引理等技術來識別非正規語言，並使用Myhill-Nerode定理進行非正規性證明。此外，還檢視了正規語言的閉包性質。

上下文無關語言是另一個重點，文本討論了上下文無關文法、喬姆斯基標準形式文法、下推自動機及其等價性。本書包括使用CNF文法和PDA分析的抽泣引理和閉包性質，並識別非上下文無關語言及理解最左推導。

圖靈機模型得到了徹底的覆蓋，解釋了各種模型和模擬。本書概述了配置、丘奇-圖靈論題，並區分遞歸語言和可遞歸枚舉語言。

可判定性和不可判定性是文本中的關鍵主題，涉及可判定問題、對角化、停機問題和萊斯定理。它還提供了可判定性的特徵，討論了Post對應問題，並檢查算術層級的較低層次。

這本教科書還深入探討計算複雜性類別，定義時間和空間複雜性類別，並呈現高效模擬和層級定理，包括Hennie-Stearns定理。它包括P和NP中的問題示例，提供對這些分類的清晰理解。

NP完全性被詳細探討，涵蓋SAT和3SAT、典範完全問題及各種NP完全問題。本書延伸至空間複雜性類別，討論PSPACE完全問題、NL完全問題，並證明NL=coNL。

最後，文本超越了NP完全性，討論Ladner的非NPC集合構造、隨機複雜性類別以及BPP和多項式層級等概念。它還檢查了多項式大小電路，提供了計算複雜性全景的全面視角。

作者簡介

Dr. Mitsunori Ogihara joined the University of Miami in 2007 as a Professor in the Department of Computer Science and as the Director of Big Data Analytics & Data Mining in the Center for Computational Science. He serves as the Director of Education and Workforce Development in the Frost Institute for Data Science (he is currently the Director of Master of Science in Data Science and Site co-Director for NSF IUCRC CARTA).

Dr. Ogihara obtained his PhD in Information Sciences from the Tokyo Institute of Technology in 1993. From 1994 to 2007, Dr. Ogihara was a Computer Science faculty member at the University of Rochester, where he was promoted to Associate Professor with tenure in 1998, and to Full Professor in 2002. He also served as Chair of the Department from 1999 to 2007.

His research interests include data mining, information retrieval, network traffic data analysis, program behavior analysis, molecular computation, and music information retrieval. A prolific scholar, Dr. Ogihara has authored/co-authored four books The Complexity Theory Companion, Music Data Mining, Exploring Data Science with R and the Tidyverse, and for Springer, Fundamentals of Java Programming, and is the author of more than 200 peer-reviewed research papers. Many papers by Dr. Ogihara are through interdisciplinary collaborations. His articles appear in journals and conferences that cover many fields, including psychology, implementation science, library science, chemistry, biology, and digital humanities. He serves as Editor-in-Chief for the Theory of Computing Systems Journal (Springer) and on the editorial board for the International Journal of Foundations of Computer Science (World Scientific).

作者簡介(中文翻譯)

小野原光則博士於2007年加入邁阿密大學，擔任計算機科學系教授及計算科學中心大數據分析與資料探勘主任。他同時擔任佛羅斯數據科學研究所的教育與勞動力發展主任（目前是數據科學碩士學位課程主任及國家科學基金會（NSF）工業聯合研究中心（IUCRC）CARTA的現場共同主任）。

小野原博士於1993年在東京科技大學獲得資訊科學博士學位。從1994年到2007年，小野原博士是羅徹斯特大學的計算機科學系教員，並於1998年晉升為終身副教授，2002年晉升為正教授。他還於1999年至2007年擔任系主任。

他的研究興趣包括資料探勘、資訊檢索、網路流量數據分析、程式行為分析、分子計算和音樂資訊檢索。作為一位多產的學者，小野原博士著有或合著四本書籍：《複雜性理論伴侶》、《音樂數據探勘》、《使用R和Tidyverse探索數據科學》，以及為Springer出版的《Java程式設計基礎》，並發表超過200篇經過同行評審的研究論文。小野原博士的許多論文都是透過跨學科合作完成的。他的文章發表在涵蓋多個領域的期刊和會議上，包括心理學、實施科學、圖書館學、化學、生物學和數位人文學。他擔任《計算系統理論期刊》（Springer）的主編，並在《計算機科學基礎國際期刊》（World Scientific）的編輯委員會中任職。

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