Forcing with random variables and proof complexity

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...

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Bibliographic Details
Main Author: Krajíček, Jan
Format: eBook
Language:English
Published: Cambridge Cambridge University Press 2011
Series:London Mathematical Society lecture note series
Subjects:
Online Access:
Collection: Cambridge Books Online - Collection details see MPG.ReNa
Description
Summary: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
Physical Description:xvi, 247 pages digital
ISBN:9781139107211