Arithmetic, Proof Theory, and Computational Complexity

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9780198536901: Arithmetic, Proof Theory, and Computational Complexity

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 *L *D 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.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

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

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

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Peter Clote (Editor), Jan Krajícek (Editor)
Editore: Oxford University Press, USA (1993)
ISBN 10: 0198536909 ISBN 13: 9780198536901
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Descrizione libro Oxford University Press, USA, 1993. Hardcover. Condizione libro: New. Codice libro della libreria DADAX0198536909

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Descrizione libro OUP Oxford, 2016. Paperback. Condizione libro: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Codice libro della libreria ria9780198536901_lsuk

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Descrizione libro Clarendon Press, 1993. HRD. Condizione libro: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria IP-9780198536901

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Descrizione libro Clarendon Press, 1993. HRD. Condizione libro: New. New Book. Delivered from our US warehouse in 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND.Established seller since 2000. Codice libro della libreria IP-9780198536901

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Descrizione libro Oxford University Press, United Kingdom, 1993. Hardback. Condizione libro: New. New.. 229 x 152 mm. Language: English . Brand New Book ***** Print on Demand *****.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 *L *D 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. Codice libro della libreria APC9780198536901

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Clote, Krajicek
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Descrizione libro Oxford University Press, United Kingdom, 1993. Hardback. Condizione libro: New. New.. 229 x 152 mm. Language: English . Brand New Book ***** Print on Demand *****. 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 *L *D 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. Codice libro della libreria APC9780198536901

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Descrizione libro OUP Oxford. Hardcover. Condizione libro: New. Hardcover. 448 pages. Dimensions: 9.0in. x 6.0in. x 1.1in.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, and similar themes, and the relations of these topics to computational complexity theory. Issuing from a two-year international collaboration, the book contains articles concerning the existence of the most general unifier, a special case of Kreisels 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, and ordinal arithmetic in L D o. Also included is an extended abstract of J. P. Ressayres new approach concerning the model completeness of the theory of real closed exponential fields. Additional features of the book include the transcription and translation of a recently discovered 1956 letter from Kurt 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); and an open problem list consisting of seven fundamental and 39 technical questions contributed by many researchers, together with a bibliography of relevant references. This scholarly work will interest mathematical logicians, proof and recursion theorists, and researchers in computational complexity. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Hardcover. Codice libro della libreria 9780198536901

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Descrizione libro Condizione libro: New. This item is Print on Demand - Depending on your location, this item may ship from the US or UK. Codice libro della libreria POD_9780198536901

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Descrizione libro Oxford University Press, 1993. Hardcover. Condizione libro: New. book. Codice libro della libreria 0198536909

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