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Look Inside Bounded Arithmetic, Propositional Logic and Complexity Theory

Bounded Arithmetic, Propositional Logic and Complexity Theory

Name: Bounded Arithmetic, Propositional Logic and Complexity Theory
Price: 151.00 USD
Availability: LimitedAvailability
ISBN: 9780511884283

$151.00 USD

Part of Encyclopedia of Mathematics and its Applications

Author: Jan Krajicek, Charles University, Prague

Date Published: February 2011
availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
format: Adobe eBook Reader
isbn: 9780511884283

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About the Authors

This book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic, with emphasis on independence proofs and lower bound proofs. The author discusses the deep connections between logic and complexity theory and lists a number of intriguing open problems. An introduction to the basics of logic and complexity theory is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. More advanced topics are then treated, including polynomial simulations and conservativity results, various witnessing theorems, the translation of bounded formulas (and their proofs) into propositional ones, the method of random partial restrictions and its applications, direct independence proofs, complete systems of partial relations, lower bounds to the size of constant-depth propositional proofs, the method of Boolean valuations, the issue of hard tautologies and optimal proof systems, combinatorics and complexity theory within bounded arithmetic, and relations to complexity issues of predicate calculus. Students and researchers in mathematical logic and complexity theory will find this comprehensive treatment an excellent guide to this expanding interdisciplinary area.
- Comprehensive treatment of an expanding subject
- Emphasis is given to independence proofs and lower bound proofs
- Completely up-to-date survey
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Reviews & endorsements
'This interesting book provides a brisk account of current research in bounded arithmetic and the complexity of propositional logic.' Mathematika
'It can be strongly recommended especially to mathematicians and computer scientists working in the field and to graduate students.' European Mathematical Society Newsletter
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Product details
- Date Published: February 2011
- format: Adobe eBook Reader
- isbn: 9780511884283
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
1. Introduction
2. Preliminaries
3. Basic complexity theory
4. Basic propositional logic
5. Basic bounded arithmetic
6. Definability of computations
7. Witnessing theorems
8. Definability and witnessing in second order theories
9. Translations of arithmetic formulas
10. Finite axiomatizability problem
11. Direct independence proofs
12. Bounds for constant-depth Frege systems
13. Bounds for Frege and extended Frege systems
14. Hard tautologies and optimal proof systems
15. Strength of bounded arithmetic
References
Index.
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