Arithmetic, Proof Theory, and Computational Complexity: 23 - Rilegato

Rilegato

ISBN 10: 0198536909 ISBN 13: 9780198536901

Casa editrice: Clarendon Press, 1993

Riassunto

This book principally concerns the rapidly growing area of what might be termed "Logical Complexity Theory", the study of bounded arithmetic, propositional proof systems, length of proof, etc and relations to computational complexity theory. Issuing from a two-year NSF and Czech Academy of Sciences grant supporting a month-long workshop and 3-day conference in San Diego (1990) and Prague (1991), the book contains refereed articles concerning the existence of the most general unifier, a special case of Kreisel's conjecture on length-of-proof, propositional logic proof size, a new alternating logtime algorithm for boolean formula evaluation and relation to branching programs, interpretability between fragments of arithmetic, feasible interpretability, provability logic, open induction, Herbrand-type theorems, isomorphism between first and second order bounded arithmetics, forcing techniques in bounded arithmetic, ordinal arithmetic in Λ Δ o . Also included is an extended abstract of J P Ressayre's new approach concerning the model completeness of the theory of real closed expotential fields. Additional features of the book include (1) the transcription and translation of a recently discovered 1956 letter from K Godel to J von Neumann, asking about a polynomial time algorithm for the proof in k-symbols of predicate calculus formulas (equivalent to the P-NP question), (2) an OPEN PROBLEM LIST consisting of 7 fundamental and 39 technical questions contributed by many researchers, together with a bibliography of relevant references.

Su questo libro

Recensione

This book is a valuable survey of the present state of research in this fascinating domain of foundational studies. It can certainly serve as an information and reference source as well as a source of problems to work on. (Journal of Logic & Computation, June '95)

This is a valuable survey of the present state of research in this fascinating domain of foundational studies. It can certainly serve as an information and reference source as well as a source of problems to work on. (Journal of Logic and Computation)

The book is on the level of a graduate course, and in this is superb. A highly recommendable book. (Mededelingen van Het Wiskundig Genootschaap, September 1996)

Contenuti

• Preface
• 1: Open Problems
• 2: Matthias Baaz: Note on the Existence of Most General Semi-unifiers
• 3: Matthias Baaz and Pavel Pudlák: Kreisel's Conjecture for L31 (including a postscript by George Kreisel)
• 4: Maria Luisa Bonet: Number of Symbols in Frege Proofs with and without the Deduction Rule
• 5: Samuel R. Buss: Algorithm for Boolean Formula Evolution and for Tree Contraction
• 6: Samuel R. Buss, Jan Kraj"icek and Gaisi Takeuti: Provably Total Functions in Bounded Arithmetic Theories Ri3, Ui2 and Vi2
• 7: Peter Clote: On Polynomial Size Frege Proofs of Certain Combinatorial Principles
• 8: Petr Hájek: Interpretability and Fragments of arithmetic
• 9: Petr Hájek, Franco Montagna and Pavel Pudlák: Abbreviating Proofs Using Metamathematical Rules
• 10: Richard Kaye: Open Induction, Tennenbaum Phenomena, and Complexity Theory
• 11: Richard Kaye: Using Herbrand-type Theorems to Separate Strong Fragments of Arithmetic
• 12: Alexander A. Razborov: An Equivalence between Second Order Bounded Domain Bounded Arithmetic and First Order Bounded Arithmetic
• 13: Jean-Pierre Ressayre: Integer Parts of Real Closed Exponential Fields (extended abstract)
• 14: Søren Riis: Making Infinite Structures Finite in Models of Second Order Bounded Arithmetic
• 15: Richard Sommer: Ordinal Arithmetic in I
• 16: Gaisi Takeuti: RSUV Isomorphism
• 17: Rineke Verbrugge: Feasible Interpretability

Dettagli dell?edizione

• Editore: Clarendon Press
• Data di pubblicazione: 1993
• Lingua: Inglese
• ISBN 10: 0198536909
• ISBN 13: 9780198536901
• Rilegatura: Copertina rigida
• Numero di pagine: 442
• Redattore: Clote Peter, Krajícek Jan
• Contatto del produttore: Oxford University Press; https://corp.oup.com/; ; WMF Platz 1; Geislingen/Steige; Baden-W?rttemberg; 73312; Germania