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Logical Foundations of Proof Complexity / Stephen Cook, Phuong Nguyen
出版者 | Cambridge : Cambridge University Press |
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出版年 | 2010 |
大きさ | 1 online resource (496 pages) : digital, PDF file(s) |
著者標目 | *Cook, Stephen author Nguyen, Phuong author |
件 名 | LCSH:Proof theory LCSH:Constructive mathematics |
一般注記 | Title from publisher's bibliographic system (viewed on 11 Nov 2016) 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 HTTP:URL=http://dx.doi.org/10.1017/CBO9780511676277 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Cambridge Books Online | 9780511676277 |
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電子リソース |
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EB00089653 |
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