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Author : Jan Krajicek
Publisher : Unknown
Page : 361 pages
File Size : 50,9 Mb
Release : 2014-05-18
Category : Computational complexity
ISBN : 1107094801
Discusses the deep connections between logic and complexity theory, and lists a number of intriguing open problems.
Author : Jan Krajicek
Publisher : Cambridge University Press
Page : 361 pages
File Size : 44,9 Mb
Release : 1995-11-24
Category : Computers
ISBN : 9780521452052
Discusses the deep connections between logic and complexity theory, and lists a number of intriguing open problems.
Author : Peter Clote,Jan Krajícek
Publisher : Clarendon Press
Page : 442 pages
File Size : 55,5 Mb
Release : 1993-05-06
Category : Mathematics
ISBN : 0198536909
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.
Author : Stephen Cook,Phuong Nguyen
Publisher : Cambridge University Press
Page : 0 pages
File Size : 48,6 Mb
Release : 2014-03-06
Category : Mathematics
ISBN : 1107694116
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.
Author : Jan Krajíček
Publisher : Cambridge University Press
Page : 533 pages
File Size : 54,6 Mb
Release : 2019-03-28
Category : Computers
ISBN : 9781108416849
Offers a self-contained work presenting basic ideas, classical results, current state of the art and possible future directions in proof complexity.
Author : Paul W. Beame
Publisher : American Mathematical Soc.
Page : 335 pages
File Size : 49,8 Mb
Release : 1998
Category : Computational complexity
ISBN : 9780821805770
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.
Author : Jan Krajíček
Publisher : Cambridge University Press
Page : 265 pages
File Size : 52,8 Mb
Release : 2010-12-23
Category : Mathematics
ISBN : 9781139493925
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.
Author : Samuel R. Buss
Publisher : Unknown
Page : 238 pages
File Size : 40,9 Mb
Release : 1986
Category : Mathematics
ISBN : UOM:39015040414040
Author : Sanjeev Arora,Boaz Barak
Publisher : Cambridge University Press
Page : 609 pages
File Size : 42,5 Mb
Release : 2009-04-20
Category : Computers
ISBN : 9780521424264
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Author : Daniel Leivant
Publisher : Springer Science & Business Media
Page : 534 pages
File Size : 42,5 Mb
Release : 1995-08-02
Category : Computers
ISBN : 3540601783
This book contains revised versions of papers invited for presentation at the International Workshop on Logic and Computational Complexity, LCC '94, held in Indianapolis, IN in October 1994. The synergy between logic and computational complexity has gained importance and vigor in recent years, cutting across many areas. The 25 revised full papers in this book contributed by internationally outstanding researchers document the state-of-the-art in this interdisciplinary field of growing interest; they are presented in sections on foundational issues, applicative and proof-theoretic complexity, complexity of proofs, computational complexity of functionals, complexity and model theory, and finite model theory.
Author : Stephen Cook,Phuong Nguyen
Publisher : Cambridge University Press
Page : 496 pages
File Size : 52,7 Mb
Release : 2010-01-25
Category : Mathematics
ISBN : 9781139486309
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.
Author : Peter Clote,Jeffrey B. Remmel
Publisher : Springer Science & Business Media
Page : 456 pages
File Size : 43,6 Mb
Release : 2013-03-13
Category : Computers
ISBN : 9781461225669
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.
Author : John P. Mayberry
Publisher : Cambridge University Press
Page : 454 pages
File Size : 55,9 Mb
Release : 2000
Category : Mathematics
ISBN : 0521770343
This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.
Author : Paul W. Beame,Samuel R. Buss
Publisher : American Mathematical Soc.
Page : 340 pages
File Size : 49,7 Mb
Release : 2024-06-25
Category : Mathematics
ISBN : 0821870823
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.
Author : Wolfgang Rautenberg
Publisher : Springer
Page : 337 pages
File Size : 46,8 Mb
Release : 2010-07-01
Category : Mathematics
ISBN : 9781441912213
Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.