Non-classical Aspects in Proof Complexity
Language: English
Published by Cuvillier Mrz 2012, 2012
- Softcover
- New
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, GermanyBuchWeltWeit Ludwig Meier e.K.
AbeBooks seller since January 11, 2012
Condition: New
£ 17.39
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This item is printed on demand - it takes 3-4 days longer - Neuware -Proof complexity focuses on the complexity of theorem proving procedures, atopic which is tightly linked to questions from computational complexity (the separation of complexity classes), first-order arithmetic theories (bounded arithmetic), and practical questions as automated theorem proving. One fascinating question in proof complexity is whether powerful computational resources as randomness or oracle access can shorten proofs or speed up proof search. In this dissertation we investigated these questions for proof systems that use a limited amount of non-uniform information (advice). This model is very interesting as¿- in contrast to the classical setting¿-it admits an optimal proof system as recently shown by Cook and Krajícek. We give a complete complexity-theoretic classification of all languages admitting polynomially bounded proof systems with advice and explore whether the advice can be simplified or even eliminated while still preserving the power of the system. Propositional proof systems enjoy a close connection to bounded arithmetic. Cook and Krajícek (JSL¿07) use the correspondence between proof systems with advice and arithmetic theories to obtain a very strong Karp-Lipton collapse result in bounded arithmetic: if SAT has polynomial-size Boolean circuits, then the polynomial hierarchy collapses to the Boolean hierarchy. Here we show that this collapse consequence is in fact optimal with respect to the theory PV, thereby answering a question of Cook and Krajícek. The second main topic of this dissertation is parameterized proof complexity, a paradigm developed by Dantchev, Martin, and Szeider (FOCS¿07) which transfers the highly successful approach of parameterized complexity to the study of proof lengths. In this thesis we introduce a powerful two player game to model and study the complexity of proofs in a tree-like Resolution system in a setting arising from parameterized complexity. This game is also applicable to show strong lower bounds in other tree-like proof systems. Moreover, we obtain the first lower bound to the general dag-like Parameterized Resolution system for the pigeonhole principle and study a variant of the DPLL algorithm in the parameterized setting. 140 pp. Englisch.…
Seller Inventory # 9783954040360
Bibliographic details
- Title
- Non-classical Aspects in Proof Complexity
- Author
- Olaf Beyersdorff
- Publisher
- Cuvillier Mrz 2012
- Publication year
- 2012
- Condition
- Neu
- Binding
- Taschenbuch
- Language
- English
- ISBN 10
- 3954040360
- ISBN 13
- 9783954040360
- Item weight
- 192 grams
- Dimensions
- 210x148x7 mm
BuchWeltWeit Ludwig Meier e.K.
Bergisch Gladbach, Germany
AbeBooks seller since January 11, 2012
Shipping rates from Germany to U.S.A.
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