Bounded Arithmetic
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Bounded Arithmetic
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Author : Samuel R. Buss
language : en
Publisher:
Release Date : 1986
Bounded Arithmetic written by Samuel R. Buss and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Bounded Arithmetic Propositional Logic And Complexity Theory
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Author : Jan Krajicek
language : en
Publisher: Cambridge University Press
Release Date : 1995-11-24
Bounded Arithmetic Propositional Logic And Complexity Theory written by Jan Krajicek and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-11-24 with Computers categories.
Discusses the deep connections between logic and complexity theory, and lists a number of intriguing open problems.
Metamathematics Of First Order Arithmetic
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Author : Petr Hájek
language : en
Publisher: Cambridge University Press
Release Date : 2017-03-02
Metamathematics Of First Order Arithmetic written by Petr Hájek and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-02 with Mathematics categories.
A much-needed monograph on the metamathematics of first-order arithmetic, paying particular attention to fragments of Peano arithmetic.
Forcing With Random Variables And Proof Complexity
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Author : Jan Krajíček
language : en
Publisher: Cambridge University Press
Release Date : 2010-12-23
Forcing With Random Variables And Proof Complexity written by Jan Krajíček and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-23 with Mathematics categories.
This book introduces a new approach to building models of bounded arithmetic, with techniques drawn from recent results in computational complexity. Propositional proof systems and bounded arithmetics are closely related. In particular, proving lower bounds on the lengths of proofs in propositional proof systems is equivalent to constructing certain extensions of models of bounded arithmetic. This offers a clean and coherent framework for thinking about lower bounds for proof lengths, and it has proved quite successful in the past. This book outlines a brand new method for constructing models of bounded arithmetic, thus for proving independence results and establishing lower bounds for proof lengths. The models are built from random variables defined on a sample space which is a non-standard finite set and sampled by functions of some restricted computational complexity. It will appeal to anyone interested in logical approaches to fundamental problems in complexity theory.
Chapters On Bounded Arithmetic On Provability Logic
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Author : Domenico Zambella
language : en
Publisher:
Release Date : 1994
Chapters On Bounded Arithmetic On Provability Logic written by Domenico Zambella and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
Proof Complexity And Feasible Arithmetics
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Author : Paul W. Beame
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Proof Complexity And Feasible Arithmetics written by Paul W. Beame and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Computational complexity categories.
The 16 papers reflect some of the breakthroughs over the past dozen years in understanding whether or not logical inferences can be made in certain situations and what resources are necessary to make such inferences, questions that play a large role in computer science and artificial intelligence. They discuss such aspects as lower bounds in proof complexity, witnessing theorems and proof systems for feasible arithmetic, algebraic and combinatorial proof systems, and the relationship between proof complexity and Boolean circuit complexity. No index. Member prices are $47 for institutions and $35 for individuals. Annotation copyrighted by Book News, Inc., Portland, OR.
Metamathematics Of First Order Arithmetic
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Author : Petr Hájek
language : en
Publisher: Cambridge University Press
Release Date : 2017-03-02
Metamathematics Of First Order Arithmetic written by Petr Hájek and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-02 with Mathematics categories.
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the third publication in the Perspectives in Logic series, is a much-needed monograph on the metamathematics of first-order arithmetic. The authors pay particular attention to subsystems (fragments) of Peano arithmetic and give the reader a deeper understanding of the role of the axiom schema of induction and of the phenomenon of incompleteness. The reader is only assumed to know the basics of mathematical logic, which are reviewed in the preliminaries. Part I develops parts of mathematics and logic in various fragments. Part II is devoted to incompleteness. Finally, Part III studies systems that have the induction schema restricted to bounded formulas (bounded arithmetic).
Systems Of Bounded Arithmetic From Descriptive Complexity Microform
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Author : Antonina Kolokolova
language : en
Publisher: Library and Archives Canada = Bibliothèque et Archives Canada
Release Date : 2005
Systems Of Bounded Arithmetic From Descriptive Complexity Microform written by Antonina Kolokolova and has been published by Library and Archives Canada = Bibliothèque et Archives Canada this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
In this thesis we discuss a general method of constructing systems of bounded arithmetic from descriptive complexity logics of known complexity. We discuss the conditions under which the resulting systems capture the same complexity class in the bounded arithmetic setting as the corresponding logic in the descriptive complexity setting. Our method works for small complexity classes (P and below) which have simple proofs of closure under complementation. Additionally, we require proofs of membership and co-membership for instances of decision problems to be constructible within the same complexity class. Based on this general theorem, we discuss systems of arithmetic for classes P and NL. We also give a system of arithmetic for SL, although the definability theorem for SL is weaker. More formally, given a logic L capturing complexity class C, the corresponding second-order system V-L of arithmetic consists of a system for AC 0 together with comprehension over L-formulae. If the class is provably in V-L closed under AC 0 reductions and every formula or its (possibly semantic) negation can be witnessed in C, then the resulting system captures C.
Bounded Gaps Between Primes
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Author : Kevin Broughan
language : en
Publisher: Cambridge University Press
Release Date : 2021-02-25
Bounded Gaps Between Primes written by Kevin Broughan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-25 with Mathematics categories.
A mathematical record of bounded prime gaps breakthroughs, from Erdős to Polymath8, with linked computer programs and complete appendices.
Arithmetic Proof Theory And Computational Complexity
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Author : Peter Clote
language : en
Publisher: Clarendon Press
Release Date : 1993-05-06
Arithmetic Proof Theory And Computational Complexity written by Peter Clote and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-05-06 with Mathematics categories.
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.