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Logical foundations of proof complexity /
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 bo...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York : Ithaca, NY :
Cambridge University Press ; Association for Symbolic Logic,
©2010.
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| Colección: | Perspectives in logic.
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| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | 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. |
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| Descripción Física: | 1 online resource (xv, 479 pages) : illustrations |
| Bibliografía: | Includes bibliographical references and index. |
| ISBN: | 9780511677168 0511677162 9780511681653 0511681658 9780511676277 0511676271 9781107694118 1107694116 1107206715 9781107206717 1282536117 9781282536111 9786612536113 661253611X 0511678428 9780511678424 0511683634 9780511683633 |