Proof Complexity And Feasible Arithmetics
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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.
Proof Complexity
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Author : Jan Krajíček
language : en
Publisher: Cambridge University Press
Release Date : 2019-03-28
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 2019-03-28 with Computers categories.
Offers a self-contained work presenting basic ideas, classical results, current state of the art and possible future directions in proof complexity.
Proof Complexity And Feasible Arithmetics
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Author : Paul W. Beame
language : en
Publisher: American Mathematical Soc.
Release Date :
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 with Mathematics categories.
Questions of mathematical proof and logical inference have been a significant thread in modern mathematics and have played a formative role in the development of computer science and artificial intelligence. Research in proof complexity and feasible theories of arithmetic aims at understanding not only whether or not logical inferences can be made but also what resources are required to carry them out. Understanding the resources required for logical inferences has major implications for some of the most important problems in computational complexity, particularly the problem of whether or not NP is equal to co-NP. In addition, these have important implications for the efficiency of automated reasoning systems. The last dozen years have seen several breakthroughs in the study of these resource requirement. Papers in this volume represent the proceedings of the DIMACS workshop on "Feasible Arithmetics and Proof Complexity" held in April 1996 in Rutgers, NJ, as part of the DIMACS Institute's Special Year on Logic and Algorithms. This book brings together some of the most recent work of leading researchers in proof complexity and feasible arithmetic reflecting many of these advances. It covers a number of aspects of the field including lower bounds in proof complexity, witnessing theorems and proof systems for feasible arithmetic, algebraic and combinatorial proof systems, interpolation theorems, and the relationship between proof complexity and Boolean circuit complexity.
Forcing With Random Variables And Proof Complexity
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Author : Jan Krajíček
language : en
Publisher:
Release Date : 2011
Forcing With Random Variables And Proof Complexity written by Jan Krajíček and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Computational complexity 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.
Logical Foundations Of Proof Complexity
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Author : Stephen Cook
language : en
Publisher: Cambridge University Press
Release Date : 2010-01-25
Logical Foundations Of Proof Complexity written by Stephen Cook 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 2010-01-25 with Mathematics categories.
This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. The result is a uniform treatment of many systems in the literature.
Feasible Mathematics Ii
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Author : Peter Clote
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-13
Feasible Mathematics Ii written by Peter Clote and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-13 with Computers categories.
Perspicuity is part of proof. If the process by means of which I get a result were not surveyable, I might indeed make a note that this number is what comes out - but what fact is this supposed to confirm for me? I don't know 'what is supposed to come out' . . . . 1 -L. Wittgenstein A feasible computation uses small resources on an abstract computa tion device, such as a 'lUring machine or boolean circuit. Feasible math ematics concerns the study of feasible computations, using combinatorics and logic, as well as the study of feasibly presented mathematical structures such as groups, algebras, and so on. This volume contains contributions to feasible mathematics in three areas: computational complexity theory, proof theory and algebra, with substantial overlap between different fields. In computational complexity theory, the polynomial time hierarchy is characterized without the introduction of runtime bounds by the closure of certain initial functions under safe composition, predicative recursion on notation, and unbounded minimization (S. Bellantoni); an alternative way of looking at NP problems is introduced which focuses on which pa rameters of the problem are the cause of its computational complexity and completeness, density and separation/collapse results are given for a struc ture theory for parametrized problems (R. Downey and M. Fellows); new characterizations of PTIME and LINEAR SPACE are given using predicative recurrence over all finite tiers of certain stratified free algebras (D.
Feasible Computations And Provable Complexity Properties
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Author : Juris Hartmanis
language : en
Publisher: SIAM
Release Date : 1978-01-01
Feasible Computations And Provable Complexity Properties written by Juris Hartmanis and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978-01-01 with Mathematics categories.
An overview of current developments in research on feasible computations; and its relation to provable properties of complexity of computations.
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.
Logical Foundations Of Proof Complexity
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Author : Stephen Cook
language : en
Publisher: Cambridge University Press
Release Date : 2010-01-25
Logical Foundations Of Proof Complexity written by Stephen Cook 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 2010-01-25 with Mathematics categories.
This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. Associated with each of many complexity classes are both a two-sorted predicate calculus theory, with induction restricted to concepts in the class, and a propositional proof system. The result is a uniform treatment of many systems in the literature, including Buss's theories for the polynomial hierarchy and many disparate systems for complexity classes such as AC0, AC0(m), TC0, NC1, L, NL, NC, and P.
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.