FORCING WITH RANDOM VARIABLES AND PROOF COMPLEXITY by Jan Krajicek ( 9780521154338 )

Item Details

Title:

FORCING WITH RANDOM VARIABLES AND PROOF COMPLEXITY

By:

Jan Krajicek

Format:

Paperback

List price:

£56.00

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£49.00

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£7.00

ISBN 10:

0521154332

ISBN 13:

9780521154338

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Publisher:

CAMBRIDGE UNIVERSITY PRESS

Pub. date:

23 December, 2010

Series:

London Mathematical Society Lecture Note Series 382

Pages:

264

Description:

A model-theoretic approach to bounded arithmetic and propositional proof complexity.

Synopsis:

This book introduces a new approach to building models of bounded arithmetic, with techniques drawn from recent results in computational complexity. Propositional proof systems and bounded arithmetics are closely related. In particular, proving lower bounds on the lengths of proofs in propositional proof systems is equivalent to constructing certain extensions of models of bounded arithmetic. This offers a clean and coherent framework for thinking about lower bounds for proof lengths, and it has proved quite successful in the past. This book outlines a brand new method for constructing models of bounded arithmetic, thus for proving independence results and establishing lower bounds for proof lengths. The models are built from random variables defined on a sample space which is a non-standard finite set and sampled by functions of some restricted computational complexity. It will appeal to anyone interested in logical approaches to fundamental problems in complexity theory.

Illustrations:

Illustrations

Publication:

Imprint:

Cambridge University Press

Returns:

Returnable

Some other items by this author:

ARITHMETIC, PROOF THEORY, AND COMPUTATIONAL COMPLEXITY (HB)

BOUNDED ARITHMETIC, PROPOSITIONAL LOGIC AND COMPLEXITY THEORY

BOUNDED ARITHMETIC, PROPOSITIONAL LOGIC AND COMPLEXITY THEORY (HB)

FORCING WITH RANDOM VARIABLES AND PROOF COMPLEXITY