Proof complexity

by Krajícek, Jan

Type Book

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Title Statements

Full title :Proof complexity / Jan Krajíček.

Summary

Proof complexity is a rich subject drawing on methods from logic, combinatorics, algebra and computer science. This self-contained book presents the basic concepts, classical results, current state of the art and possible future directions in the field. It stresses a view of proof complexity as a whole entity rather than a collection of various topics held together loosely by a few notions, and it favors more generalizable statements. Lower bounds for lengths of proofs, often regarded as the key issue in proof complexity, are of course covered in detail. However, upper bounds are not neglected: this book also explores the relations between bounded arithmetic theories and proof systems and how they can be used to prove upper bounds on lengths of proofs and simulations among proof systems. It goes on to discuss topics that transcend specific proof systems, allowing for deeper understanding of the fundamental problems of the subject.

Edition Statements

Publication Date:2019.

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:Cambridge, United Kingdom
Language:eng
Publication Date:2019.

The Physical Object

Description:1 online resource

Edition Identifiers

ISBN:9781108271585, 1108271588, 9781108242066, 1108242065, 9781108416849, 1108416845
oclc:on1090812743
LC Classification:QA9.54
Dewey Decimal:511.3/6

Concepts and problems -- Frege systems -- Sequent calculus -- Quantifed propositional calculus -- Resolution -- Algebraic and geometric proof systems -- Further proof systems -- Basic example of the correspondence -- Two worlds of bounded arithmetic -- Up to EF via the <...> translation -- Examples of upper bounds and p-simulations -- Beyond EF via the || ... || translation -- R and R-like proof systems -- LKD+1/2 and combinatorial restrictions -- Fd and logical restrictions -- Algebraic and geometric proof systems -- Feasible interpolation: a framework -- Feasible interpolation: applications -- Hard tautologies -- Model theory and lower bounds -- Optimality -- The nature of proof complexity.