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The Resource Theory of computation, Dexter C. Kozen

Theory of computation, Dexter C. Kozen

Creator
Summary
In these early years of the 21st Century, researchers in the field of computing are delving ever further into the new possibilities of the science and to the primary tools that form its foundations. The theory behind computation has never been more important. Theory of Computation is a unique textbook that serves the dual purposes of covering core material in the foundations of computing, as well as providing an introduction to some more advanced contemporary topics. This innovative text focuses primarily, although by no means exclusively, on computational complexity theory: the classification of computational problems in terms of their inherent complexity. It incorporates rigorous treatment of computational models, such as deterministic, nondeterministic, and alternating Turing machines; circuits; probabilistic machines; interactive proof systems; automata on infinite objects; and logical formalisms. Although the complexity universe stops at polynomial space in most treatments, this work also examines higher complexity levels all the way up through primitive and partial recursive functions and the arithmetic and analytic hierarchies. Topics and features: {u2022} Provides in-depth coverage of both classical and contemporary approaches in one useful, concise volume {u2022} Organized into readily applicable, self-contained primary and secondary lectures {u2022} Contains more than 180 homework exercises of varying difficulty levels, many with hints and solutions {u2022} Includes approximation and inapproximation results, and some lower bounds {u2022} Treats complexity theory and classical recursion theory in a unified framework Advanced undergraduates and first-year graduates in Computer Science or Mathematics will receive a thorough grounding in the core theory of computation and computational complexity, as well as an introduction to advanced contemporary topics for further study. Computing professionals and other scientists interested in learning more about these topics will also find this text extremely useful. Prof. Dexter Kozen teaches at Cornell University, Ithaca, New York, and has comprehensively class-tested this book's content. He authored the highly successful Automata and Computability, which offers an introduction to the basic theoretical models of computability, and The Design and Analysis of Algorithms
Language
eng
Work
Publication
Extent
1 online resource (xiii, 418 pages)
Contents
  • Lectures
  • The Complexity of Computations
  • Time and Space Complexity Classes and Savitch's Theorem
  • Separation Results
  • The Immerman-Szelepcsényi Theorem
  • Logspace Computability
  • The Circuit Value Problem
  • The Knaster-Tarski Theorem
  • Alternation
  • Problems Complete for PSPACE
  • The Polynomial-Time Hierarchy
  • More on the Polynomial-Time Hierarchy
  • Parallel Complexity
  • Relation of NC to Time-Space Classes
  • Probabilistic Complexity
  • BPP?2P??2P
  • Chinese Remaindering
  • Complexity of Primality Testing
  • Berlekamp's Algorithm
  • Interactive Proofs
  • PSPACE IP
  • IP PSPACE
  • Probabilistically Checkable Proofs
  • NP PCP(n3, 1)
  • More on PCP
  • A Crash Course in Logic
  • Complexity of Decidable Theories
  • Complexity of the Theory of Real Addition
  • Lower Bound for the Theory of Real Addition
  • Lower Bound for Integer Addition
  • Automata on Infinite Strings and S1S
  • Determinization of?-Automata
  • Safra's Construction
  • Relativized Complexity
  • Nonexistence of Sparse Complete Sets
  • Unique Satisfiability
  • Toda's Theorem
  • Circuit Lower Bounds and Relativized PSPACE = PH
  • Lower Bounds for Constant Depth Circuits
  • The Switching Lemma
  • Tail Bounds
  • The Gap Theorem and Other Pathology
  • Partial Recursive Functions and Gödel Numberings
  • Applications of the Recursion Theorem
  • Abstract Complexity
  • The Arithmetic Hierarchy
  • Complete Problems in the Arithmetic Hierarchy
  • Post's Problem
  • The Friedberg-Muchnik Theorem
  • The Analytic Hierarchy
  • Kleene's Theorem
  • Fair Termination and Harel's Theorem
  • Exercises
  • Homework 1
  • Homework 2
  • Homework 3
  • Homework 4
  • Homework 5
  • Homework 6
  • Homework 7
  • Homework 8
  • Homework 9
  • Homework 10
  • Homework 11
  • Homework 12
  • Miscellaneous Exercises
  • Hints and Solutions
  • Homework 1 Solutions
  • Homework 2 Solutions
  • Homework 3 Solutions
  • Homework 4 Solutions
  • Homework 5 Solutions
  • Homework 6 Solutions
  • Homework 7 Solutions
  • Homework 8 Solutions
  • Homework 9 Solutions
  • Homework 10 Solutions
  • Homework 11 Solutions
  • Homework 12 Solutions
  • Hints for Selected Miscellaneous Exercises
  • Solutions to Selected Miscellaneous Exercises
Isbn
9781846282973
Instance
Label
Theory of computation
Title
Theory of computation
Statement of responsibility
Dexter C. Kozen
Creator
Subject
Language
eng
Summary
In these early years of the 21st Century, researchers in the field of computing are delving ever further into the new possibilities of the science and to the primary tools that form its foundations. The theory behind computation has never been more important. Theory of Computation is a unique textbook that serves the dual purposes of covering core material in the foundations of computing, as well as providing an introduction to some more advanced contemporary topics. This innovative text focuses primarily, although by no means exclusively, on computational complexity theory: the classification of computational problems in terms of their inherent complexity. It incorporates rigorous treatment of computational models, such as deterministic, nondeterministic, and alternating Turing machines; circuits; probabilistic machines; interactive proof systems; automata on infinite objects; and logical formalisms. Although the complexity universe stops at polynomial space in most treatments, this work also examines higher complexity levels all the way up through primitive and partial recursive functions and the arithmetic and analytic hierarchies. Topics and features: {u2022} Provides in-depth coverage of both classical and contemporary approaches in one useful, concise volume {u2022} Organized into readily applicable, self-contained primary and secondary lectures {u2022} Contains more than 180 homework exercises of varying difficulty levels, many with hints and solutions {u2022} Includes approximation and inapproximation results, and some lower bounds {u2022} Treats complexity theory and classical recursion theory in a unified framework Advanced undergraduates and first-year graduates in Computer Science or Mathematics will receive a thorough grounding in the core theory of computation and computational complexity, as well as an introduction to advanced contemporary topics for further study. Computing professionals and other scientists interested in learning more about these topics will also find this text extremely useful. Prof. Dexter Kozen teaches at Cornell University, Ithaca, New York, and has comprehensively class-tested this book's content. He authored the highly successful Automata and Computability, which offers an introduction to the basic theoretical models of computability, and The Design and Analysis of Algorithms
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorDate
1951-
http://library.link/vocab/creatorName
Kozen, Dexter
Dewey number
511.352
Illustrations
illustrations
Index
index present
LC call number
QA267.7
LC item number
.K69 2006eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Texts in computer science
http://library.link/vocab/subjectName
  • Computational complexity
  • Computer science
  • Recursion theory
  • Computer science
  • Recursion theory
  • Mathematische programmering
  • Computational complexity
  • Informatique
  • Computational complexity
  • Computer science
  • Recursion theory
  • Mathematische programmering
Label
Theory of computation, Dexter C. Kozen
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 391-398) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Lectures -- The Complexity of Computations -- Time and Space Complexity Classes and Savitch's Theorem -- Separation Results -- The Immerman-Szelepcsényi Theorem -- Logspace Computability -- The Circuit Value Problem -- The Knaster-Tarski Theorem -- Alternation -- Problems Complete for PSPACE -- The Polynomial-Time Hierarchy -- More on the Polynomial-Time Hierarchy -- Parallel Complexity -- Relation of NC to Time-Space Classes -- Probabilistic Complexity -- BPP?2P??2P -- Chinese Remaindering -- Complexity of Primality Testing -- Berlekamp's Algorithm -- Interactive Proofs -- PSPACE IP -- IP PSPACE -- Probabilistically Checkable Proofs -- NP PCP(n3, 1) -- More on PCP -- A Crash Course in Logic -- Complexity of Decidable Theories -- Complexity of the Theory of Real Addition -- Lower Bound for the Theory of Real Addition -- Lower Bound for Integer Addition -- Automata on Infinite Strings and S1S -- Determinization of?-Automata -- Safra's Construction -- Relativized Complexity -- Nonexistence of Sparse Complete Sets -- Unique Satisfiability -- Toda's Theorem -- Circuit Lower Bounds and Relativized PSPACE = PH -- Lower Bounds for Constant Depth Circuits -- The Switching Lemma -- Tail Bounds -- The Gap Theorem and Other Pathology -- Partial Recursive Functions and Gödel Numberings -- Applications of the Recursion Theorem -- Abstract Complexity -- The Arithmetic Hierarchy -- Complete Problems in the Arithmetic Hierarchy -- Post's Problem -- The Friedberg-Muchnik Theorem -- The Analytic Hierarchy -- Kleene's Theorem -- Fair Termination and Harel's Theorem -- Exercises -- Homework 1 -- Homework 2 -- Homework 3 -- Homework 4 -- Homework 5 -- Homework 6 -- Homework 7 -- Homework 8 -- Homework 9 -- Homework 10 -- Homework 11 -- Homework 12 -- Miscellaneous Exercises -- Hints and Solutions -- Homework 1 Solutions -- Homework 2 Solutions -- Homework 3 Solutions -- Homework 4 Solutions -- Homework 5 Solutions -- Homework 6 Solutions -- Homework 7 Solutions -- Homework 8 Solutions -- Homework 9 Solutions -- Homework 10 Solutions -- Homework 11 Solutions -- Homework 12 Solutions -- Hints for Selected Miscellaneous Exercises -- Solutions to Selected Miscellaneous Exercises
Control code
209949299
Dimensions
unknown
Extent
1 online resource (xiii, 418 pages)
Form of item
online
Isbn
9781846282973
Lccn
2005937504
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/1-84628-477-5
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-1-84628-297-3
Specific material designation
remote
System control number
(OCoLC)209949299
Label
Theory of computation, Dexter C. Kozen
Publication
Bibliography note
Includes bibliographical references (pages 391-398) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Lectures -- The Complexity of Computations -- Time and Space Complexity Classes and Savitch's Theorem -- Separation Results -- The Immerman-Szelepcsényi Theorem -- Logspace Computability -- The Circuit Value Problem -- The Knaster-Tarski Theorem -- Alternation -- Problems Complete for PSPACE -- The Polynomial-Time Hierarchy -- More on the Polynomial-Time Hierarchy -- Parallel Complexity -- Relation of NC to Time-Space Classes -- Probabilistic Complexity -- BPP?2P??2P -- Chinese Remaindering -- Complexity of Primality Testing -- Berlekamp's Algorithm -- Interactive Proofs -- PSPACE IP -- IP PSPACE -- Probabilistically Checkable Proofs -- NP PCP(n3, 1) -- More on PCP -- A Crash Course in Logic -- Complexity of Decidable Theories -- Complexity of the Theory of Real Addition -- Lower Bound for the Theory of Real Addition -- Lower Bound for Integer Addition -- Automata on Infinite Strings and S1S -- Determinization of?-Automata -- Safra's Construction -- Relativized Complexity -- Nonexistence of Sparse Complete Sets -- Unique Satisfiability -- Toda's Theorem -- Circuit Lower Bounds and Relativized PSPACE = PH -- Lower Bounds for Constant Depth Circuits -- The Switching Lemma -- Tail Bounds -- The Gap Theorem and Other Pathology -- Partial Recursive Functions and Gödel Numberings -- Applications of the Recursion Theorem -- Abstract Complexity -- The Arithmetic Hierarchy -- Complete Problems in the Arithmetic Hierarchy -- Post's Problem -- The Friedberg-Muchnik Theorem -- The Analytic Hierarchy -- Kleene's Theorem -- Fair Termination and Harel's Theorem -- Exercises -- Homework 1 -- Homework 2 -- Homework 3 -- Homework 4 -- Homework 5 -- Homework 6 -- Homework 7 -- Homework 8 -- Homework 9 -- Homework 10 -- Homework 11 -- Homework 12 -- Miscellaneous Exercises -- Hints and Solutions -- Homework 1 Solutions -- Homework 2 Solutions -- Homework 3 Solutions -- Homework 4 Solutions -- Homework 5 Solutions -- Homework 6 Solutions -- Homework 7 Solutions -- Homework 8 Solutions -- Homework 9 Solutions -- Homework 10 Solutions -- Homework 11 Solutions -- Homework 12 Solutions -- Hints for Selected Miscellaneous Exercises -- Solutions to Selected Miscellaneous Exercises
Control code
209949299
Dimensions
unknown
Extent
1 online resource (xiii, 418 pages)
Form of item
online
Isbn
9781846282973
Lccn
2005937504
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/1-84628-477-5
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-1-84628-297-3
Specific material designation
remote
System control number
(OCoLC)209949299

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