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Arithmetic, Proof Theory, and Computational Complexity (Oxford L
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Item specifics
- Condition
- Title
- Arithmetic, Proof Theory, and Computational Complexity (Oxford L
- ISBN
- 9780198536901
- Subject Area
- Mathematics, Computers
- Publication Name
- Arithmetic, Proof Theory, and Computational Complexity
- Publisher
- Oxford University Press, Incorporated
- Item Length
- 9.5 in
- Subject
- Machine Theory, Logic, Arithmetic
- Publication Year
- 1993
- Series
- Oxford Logic Guides
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Item Height
- 1.2 in
- Item Weight
- 28.6 Oz
- Item Width
- 6.4 in
- Number of Pages
- 442 Pages
About this product
Product Identifiers
Publisher
Oxford University Press, Incorporated
ISBN-10
0198536909
ISBN-13
9780198536901
eBay Product ID (ePID)
1412592
Product Key Features
Number of Pages
442 Pages
Language
English
Publication Name
Arithmetic, Proof Theory, and Computational Complexity
Subject
Machine Theory, Logic, Arithmetic
Publication Year
1993
Type
Textbook
Subject Area
Mathematics, Computers
Series
Oxford Logic Guides
Format
Hardcover
Dimensions
Item Height
1.2 in
Item Weight
28.6 Oz
Item Length
9.5 in
Item Width
6.4 in
Additional Product Features
Intended Audience
College Audience
LCCN
92-041659
Dewey Edition
20
Reviews
'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, '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, '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 and 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
Series Volume Number
23
Illustrated
Yes
Dewey Decimal
511.3
Table Of Content
Preface1. Open Problems2. Note on the Existence of Most General Semi-unifiers3. Kreisel's Conjecture for L31 (including a postscript by George Kreisel)4. Number of Symbols in Frege Proofs with and without the Deduction Rule5. Algorithm for Boolean Formula Evolution and for Tree Contraction6. Provably Total Functions in Bounded Arithmetic Theories Ri3, Ui2 and Vi27. On Polynomial Size Frege Proofs of Certain Combinatorial Principles8. Interpretability and Fragments of arithmetic9. Abbreviating Proofs Using Metamathematical Rules10. Open Induction, Tennenbaum Phenomena, and Complexity Theory11. Using Herbrand-type Theorems to Separate Strong Fragments of Arithmetic12. An Equivalence between Second Order Bounded Domain Bounded Arithmetic and First Order Bounded Arithmetic13. Integer Parts of Real Closed Exponential Fields (extended abstract)14. Making Infinite Structures Finite in Models of Second Order Bounded Arithmetic15. Ordinal Arithmetic in I16. RSUV Isomorphism17. Feasible Interpretability
Synopsis
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., 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 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, and 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 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 book principally concerns the rapidly growing area of "Logical Complexity Theory", the study of bounded arithmetic, propositional proof systems, length of proof, etc and relations to computational complexity theory. 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., 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 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, and ordinal arithmetic in [o. Also included is an extended abstract of J.P. Ressayre's 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.
Copyright Date
1993
ebay_catalog_id
4
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