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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Bibliographic Details
Main Author Maruoka, Akira
Format eBook Book
LanguageEnglish
Published London Springer Nature 2011
Springer
Springer London, Limited
Springer London
Edition1
Subjects
Computational complexity
Computational Science and Engineering
Computer Science
Data processing Computer science
Logic, Symbolic and mathematical
Machine theory
Mathematics
Theory of Computation
Online AccessGet full text
ISBN0857295357
9780857295354
0857295349
9780857295347
DOI10.1007/978-0-85729-535-4

Cover

Table of Contents:
  • 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