Bounded arithmetic, propositional logic, and complexity theory

著者

• Krajíček, Jan

書誌事項

Bounded arithmetic, propositional logic, and complexity theory

Jan Krajíček

（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 60）

Cambridge University Press, 1995

注記

Includes bibliographical references (p. 327-334) and indexes

内容説明・目次

内容説明

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 theory is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. More advanced topics are then 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, direct independence proofs, complete systems of partial relations, lower bounds to the size of constant-depth propositional proofs, the method of Boolean valuations, the issue of hard tautologies and optimal proof systems, 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 this comprehensive treatment an excellent guide to this expanding interdisciplinary area.

目次

• 1. Introduction
• 2. Preliminaries
• 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
• References
• Index.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BA26572058
• ISBN:
  • 0521452058
• LCCN: 94047054
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cambridge, England ; New York
• ページ数/冊数: xiv, 343 p.
• 大きさ: 24 cm
• 分類:
  • LCC : QA9.56
  • DC20 : 511.3
  • NDC8 : 410.96
• 件名:
  • LCSH : Constructive mathematics
  • LCSH : Proposition (Logic)
  • LCSH : Computational complexity
• 親書誌ID:
  • BA00064663