Stephen Cook

Logical Foundations of Proof Complexity (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. Associated with each of many complexity classes are both a two-sorted predicate calculus theory, with induction restricted to concepts in the class, and a propositional proof system. The complexity classes range from AC0 for the weakest theory up to the polynomial hierarchy. Each bounded theorem in a theory translates into a family of (quantified) propositional tautologies with polynomial size proofs in the corresponding proof system. The theory proves the soundness of the associated proof system. The result is a uniform treatment of many systems in the literature, including Buss's theories for the polynomial hierarchy and many disparate systems for complexity classes such as AC0, AC0(m), TC0, NC1, L, NL, NC, and P.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 25. Januar 2010
• Englisch
• ISBN-13: 9780511686146
• Artikelnr.: 38206313

Autorenporträt

Stephen Cook is a journalist and author with extensive experience in national newspapers and magazines, including 18 years at The Guardian. He has published five novels and two non-fiction books.

Inhaltsangabe

1. Introduction
2. The predicate calculus and the system
3. Peano arithmetic and its subsystems
4. Two-sorted logic and complexity classes
5. The theory V0 and AC0
6. The theory V1 and polynomial time
7. Propositional translations
8. Theories for polynomial time and beyond
9. Theories for small classes
10. Proof systems and the reflection principle
11. Computation models.