Concise Guide to Computation Theory
Combining lucid description and illustrations with rigorous arguments and detailed proofs, this book examines the core concepts of automata and languages, computability, and complexity of computation, and offers a solid foundation in computation theory.
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| Main Author | |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
London
Springer Nature
2011
Springer Springer London, Limited Springer London |
| Edition | 1 |
| Subjects | |
| Online Access | Get full text |
| ISBN | 0857295357 9780857295354 0857295349 9780857295347 |
| DOI | 10.1007/978-0-85729-535-4 |
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| Abstract | Combining lucid description and illustrations with rigorous arguments and detailed proofs, this book examines the core concepts of automata and languages, computability, and complexity of computation, and offers a solid foundation in computation theory. |
|---|---|
| AbstractList | Combining lucid description and illustrations with rigorous arguments and detailed proofs, this book examines the core concepts of automata and languages, computability, and complexity of computation, and offers a solid foundation in computation theory. Presents a detailed introduction to the theory of computation, complete with concise explanations of the mathematical prerequisites Provides end-of-chapter problems with solutions, in addition to chapter-opening summaries and numerous examples and definitions throughout the text Draws upon the author's extensive teaching experience and broad research interests. |
| Author | Maruoka, Akira |
| Author_FL | マルオカ, アキラ |
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| Copyright | Springer-Verlag London Limited 2011 |
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| DOI | 10.1007/978-0-85729-535-4 |
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| Notes | Includes bibliographical references (p. 273-276) and index |
| OCLC | 728098402 |
| PQID | EBC5555124 |
| PageCount | 285 |
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| Snippet | Combining lucid description and illustrations with rigorous arguments and detailed proofs, this book examines the core concepts of automata and languages,... Presents a detailed introduction to the theory of computation, complete with concise explanations of the mathematical prerequisites Provides end-of-chapter... |
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| SubjectTerms | Computational complexity Computational Science and Engineering Computer Science Data processing Computer science Logic, Symbolic and mathematical Machine theory Mathematics Theory of Computation |
| TableOfContents | Intro -- Concise Guide to Computation Theory -- Endorsements -- Foreword -- Preface to the English Edition -- Preface -- Contents -- Part I: The Theory of Computation -- Chapter 1: Everything Begins with Computation -- 1.1 Computational Barrier -- Computational Limit in Principle -- Practical Limit of Computation -- Barrier from Computational Models -- 1.2 Propriety of Computational Models -- Robustness of Computational Model -- Development of Computational Models -- 1.3 Using this Book Efficiently -- Chapter 2: Preliminaries to the Theory of Computation -- 2.1 Set -- 2.2 Strings and Languages -- 2.3 Functions and Problems -- 2.4 Relations and Graphs -- 2.5 Boolean Operations and Boolean Formulas -- 2.6 Propositions and Proofs -- 2.7 Descriptions of Algorithms -- 2.8 Problems -- Part II: Automata and Languages -- Chapter 3: Finite Automata -- 3.1 Modeling by Automata -- Modeling of Problems -- Definition of a Finite Automaton -- 3.2 Nondeterministic Finite Automaton -- Generalization to a Nondeterministic Finite Automaton -- Equivalence of Deterministic and Nondeterministic Automata -- 3.3 Regular Expression -- Definition of a Regular Expression -- Equivalence of Regular Expression and Finite Automaton -- 3.4 Properties of Regular Languages -- Limit of Language Accepting Power of a Finite Automaton -- Closure Properties of the Class of Regular Languages -- 3.5 Problems -- Chapter 4: Context-Free Languages -- 4.1 Context-Free Grammar -- 4.2 Generating and Accepting -- 4.3 Chomsky Normal Form -- 4.4 Limitation on Generating Power of Context-Free Grammars -- 4.5 Membership Problem for Context-Free Languages -- 4.6 Problems -- Chapter 5: Pushdown Automata -- 5.1 Pushdown Automaton -- 5.2 Equivalence of Pushdown Automaton and Context-Free Grammar -- Simulating a Context-Free Grammar by a Pushdown Automaton 11.5 Chapter 6 -- 11.6 Chapter 7 -- 11.7 Chapter 8 -- 11.8 Chapter 9 -- 11.9 Chapter 10 -- Chapter 12: Concluding Remarks -- Bibliography -- References -- Index Simulating a Pushdown Automaton by a Context-Free Grammar -- 5.3 Problems -- Part III: Computability -- Chapter 6: Turing Machine -- 6.1 Turing Machine -- Examples of Turing Machines -- 6.2 Variants of Turing Machines -- Simulating Bilaterally Infinite Tape TM by Unilaterally Infinite Tape TM -- Simulating Multitape TM by Single-Tape TM -- 6.3 Nondeterministic Turing Machines -- 6.4 Church-Turing Thesis -- 6.5 Problems -- Chapter 7: Universality of Turing Machine and Its Limitations -- 7.1 Universal Turing Machine -- 7.2 Undecidability of the Halting Problem -- 7.3 Reduction -- 7.4 Undecidability of Post Correspondence Problem -- 7.5 Problems -- Part IV: Complexity of Computation -- Chapter 8: Computational Complexity Based on Turing Machines -- 8.1 Time Complexity -- Time Required to Check Well-Nested Parentheses -- Big-O Notation -- Time Complexity of Turing Machines and that of Problems -- 8.2 Problems that Are Solvable in Polynomial Time and those that Have not Been Solved in Polynomial Time -- Reachability Problem -- Eulerian Path Problem -- Hamiltonian Path Problem -- 8.3 P and NP -- 8.4 Problems -- Chapter 9: Computational Complexity Based on Boolean Circuits -- 9.1 Boolean Functions and Boolean Circuits -- 9.2 Finite Functions and Finite Circuits -- 9.3 Boolean Circuit Family to Simulate Deterministic Turing Machine -- 9.4 Finite Circuit Family to Simulate Nondeterministic Turing Machine -- 9.5 Satisfiability Problems -- 9.6 Reducing Circuit Satisfiability Problem to Formula Satisfiability Problem -- 9.7 Problems -- Chapter 10: NP-Completeness -- 10.1 NP-Completeness -- 10.2 NP-Complete Problems -- Satisfiability Problem -- Hamiltonian Path Problem -- Subset Sum Problem -- 10.3 Problems -- Part V: Conclusions and Exercise Solutions -- Chapter 11: Solutions -- 11.1 Chapter 2 -- 11.2 Chapter 3 -- 11.3 Chapter 4 -- 11.4 Chapter 5 |
| Title | Concise Guide to Computation Theory |
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