Overview
- Includes exercises at end of each chapter
- Authors website will be maintained for corrections, exercises, remarks and updates
- Describes a logical approach to complexity theory, for computer scientists
- Presents new material, close to the current research
- Unifies with a common notation many areas of theoretical computer science
- Includes supplementary material: sn.pub/extras
Part of the book series: Discrete Mathematics and Theoretical Computer Science (DISCMATH)
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Table of contents (19 chapters)
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Front Matter
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Introduction
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Basic model theory and computability
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Front Matter
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Descriptive Complexity
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Front Matter
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Approximation and classes beyond NP
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Front Matter
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Keywords
About this book
Logic and Complexity looks at basic logic as it is used in Computer Science, and provides students with a logical approach to Complexity theory. With plenty of exercises, this book presents classical notions of mathematical logic, such as decidability, completeness and incompleteness, as well as new ideas brought by complexity theory such as NP-completeness, randomness and approximations, providing a better understanding for efficient algorithmic solutions to problems.
Divided into three parts, it covers:
- Model Theory and Recursive Functions - introducing the basic model theory of propositional, 1st order, inductive definitions and 2nd order logic. Recursive functions, Turing computability and decidability are also examined.
- Descriptive Complexity - looking at the relationship between definitions of problems, queries, properties of programs and their computational complexity.
- Approximation - explaining how some optimization problems and counting problems can be approximated according to their logical form.
Logic is important in Computer Science, particularly for verification problems and database query languages such as SQL. Students and researchers in this field will find this book of great interest.
Authors and Affiliations
Bibliographic Information
Book Title: Logic and Complexity
Authors: Richard Lassaigne, Michel Rougemont
Series Title: Discrete Mathematics and Theoretical Computer Science
DOI: https://doi.org/10.1007/978-0-85729-392-3
Publisher: Springer London
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag London 2004
Hardcover ISBN: 978-1-85233-565-6Published: 20 January 2004
Softcover ISBN: 978-1-4471-1052-1Published: 08 October 2012
eBook ISBN: 978-0-85729-392-3Published: 06 December 2012
Edition Number: 1
Number of Pages: X, 361
Topics: Discrete Mathematics in Computer Science, Computer System Implementation, Mathematical Logic and Foundations, Probability Theory and Stochastic Processes, Calculus of Variations and Optimal Control; Optimization, Logics and Meanings of Programs