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This book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic with emphasis on independence proofs and lower bound proofs. The author discusses the deep connections between logic and complexity theory and lists a number of intriguing open problems. An introduction to the basics of logic and complexity is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. Then more advanced topics are treated, including polynomial simulations and conservativity results, various witnessing theorems, the translation of bounded formulas (and their proofs) into propositional ones, the method of random partial restrictions and its applications, simple independence proofs, complete systems of partial relations, lower bounds to the size of constant-depth propositional proofs, the approximation method and the method of Boolean valuations, combinatorics and complexity theory within bounded arithmetic, and relations to complexity issues of predicate calculus. Students and researchers in mathematical logic and complexity theory will find his comprehensive treatment an excellent guide to this expanding interdisciplinary area.Read more
- Comprehensive treatment of an expanding subject
- Emphasis is given to independence proofs and lower bound proofs
- Completely up-to-date survey
Reviews & endorsements
"...the author has produced a very good piece of work, which can be strongly recommended to anyone wishing to study the relations between bounded arithmetic and complexity of propositional logic." Constantine DimitracopoulosSee more reviews
"...a mathematical masterpiece...presents students and researchers with the most important tools, general background and literature references to begin research in this exciting new area in the intersection of mathematical logic, theoretical computer science, and finite combinatorics...a major accomplishment...will play a substantial role in the training of future researchers." Journal of Symbolic Logic
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- Date Published: November 1995
- format: Hardback
- isbn: 9780521452052
- length: 360 pages
- dimensions: 242 x 162 x 27 mm
- weight: 0.65kg
- availability: Available
Table of Contents
3. Basic complexity theory
4. Basic propositional logic
5. Basic bounded arithmetic
6. Definability of computations
7. Witnessing theorems
8. Definability and witnessing in second order theories
9. Translations of arithmetic formulas
10. Finite axiomatizability problem
11. Direct independence proofs
12. Bounds for constant-depth Frege systems
13. Bounds for Frege and extended Frege systems
14. Hard tautologies and optimal proof systems
15. Strength of bounded arithmetic
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