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[ 洋図書 ] Proof complexity / ( Encyclopedia of mathematics and its applications ; 170 )

Jan Krajíček, Charles University, Prague. -- Cambridge University Press, -- 2019, --

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ISBN 1108416845 (hardcover ; alkaline paper)
ISBN13桁 9781108416849 (hardcover ; alkaline paper)
テキストの言語 英語                  
分類：NDC10版 410.8
個人著者標目 Krajíček, Jan.
本タイトル Proof complexity /
著者名 Jan Krajíček, Charles University, Prague.
出版地・頒布地 Cambridge, United Kingdom ;
出版者・頒布者名 Cambridge University Press,
出版年・頒布年 2019,
数量 xiv, 516 pages ;
大きさ 24 cm.
書誌注記 Includes bibliographical references (pages [481]-505) and index.
内容注記 Concepts and problems -- Frege systems -- Sequent calculus -- Quantifed propositional calculus -- Resolution -- Algebraic and geometric proof systems -- Further proof systems -- Basic example of the correspondence between theories and proof systems -- 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.
要約、抄録、注釈等 "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"-- Provided by publisher.
統一タイトル(シリーズ副出標目) Encyclopedia of mathematics and its applications ;
シリーズの巻次 v. 170.
シリーズ名・巻次 Encyclopedia of mathematics and its applications ; 170
一般件名 Proof theory.
Computational complexity.
資料情報1 『Proof complexity /』（Encyclopedia of mathematics and its applications ; 170）　Jan Krajíček, Charles University, Prague.　Cambridge University Press,　2019, （所蔵館：中央　 請求記号：F/410.8/E56/E1-170　 資料コード：7111986385）
URL https://catalog.library.metro.tokyo.lg.jp/winj/opac/switch-detail.do?lang=ja&bibid=1352037299

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