Forcing with Random Variables and Proof Complexity

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Publisher :
ISBN 13 : 9781139123082
Total Pages : 247 pages
Book Rating : 4.1/5 (23 download)

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Book Synopsis Forcing with Random Variables and Proof Complexity by : Jan Krajíček

Download or read book Forcing with Random Variables and Proof Complexity written by Jan Krajíček and published by . This book was released on 2011 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Forcing with Random Variables and Proof Complexity

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Publisher :
ISBN 13 : 9781139127998
Total Pages : 266 pages
Book Rating : 4.1/5 (279 download)

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Book Synopsis Forcing with Random Variables and Proof Complexity by : Jan Krajíček

Download or read book Forcing with Random Variables and Proof Complexity written by Jan Krajíček and published by . This book was released on 2014-05-14 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: A model-theoretic approach to bounded arithmetic and propositional proof complexity.

Forcing with Random Variables and Proof Complexity

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Publisher : Cambridge University Press
ISBN 13 : 1139493922
Total Pages : 265 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Forcing with Random Variables and Proof Complexity by : Jan Krajíček

Download or read book Forcing with Random Variables and Proof Complexity written by Jan Krajíček and published by Cambridge University Press. This book was released on 2010-12-23 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Approaches to Computational Barriers

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Publisher : Springer Science & Business Media
ISBN 13 : 3540354662
Total Pages : 623 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Logical Approaches to Computational Barriers by : Arnold Beckmann

Download or read book Logical Approaches to Computational Barriers written by Arnold Beckmann and published by Springer Science & Business Media. This book was released on 2006-06-26 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Second International Conference on Computability in Europe, CiE 2006, held in Swansea, UK, June/July 2006. The book presents 31 revised full papers together with 30 invited papers, including papers corresponding to 8 plenary talks and 6 special sessions on proofs and computation, computable analysis, challenges in complexity, foundations of programming, mathematical models of computers and hypercomputers, and Gödel centenary: Gödel's legacy for computability.

Proof Complexity

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Publisher : Cambridge University Press
ISBN 13 : 1108416845
Total Pages : 533 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Proof Complexity by : Jan Krajíček

Download or read book Proof Complexity written by Jan Krajíček and published by Cambridge University Press. This book was released on 2019-03-28 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a self-contained work presenting basic ideas, classical results, current state of the art and possible future directions in proof complexity.

Logic, Automata, and Computational Complexity

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Publisher : Morgan & Claypool
ISBN 13 :
Total Pages : 424 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Logic, Automata, and Computational Complexity by : Bruce M. Kapron

Download or read book Logic, Automata, and Computational Complexity written by Bruce M. Kapron and published by Morgan & Claypool. This book was released on 2023-05-22 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Professor Stephen A. Cook is a pioneer of the theory of computational complexity. His work on NP-completeness and the P vs. NP problem remains a central focus of this field. Cook won the 1982 Turing Award for “his advancement of our understanding of the complexity of computation in a significant and profound way.” This volume includes a selection of seminal papers embodying the work that led to this award, exemplifying Cook’s synthesis of ideas and techniques from logic and the theory of computation including NP-completeness, proof complexity, bounded arithmetic, and parallel and space-bounded computation. These papers are accompanied by contributed articles by leading researchers in these areas, which convey to a general reader the importance of Cook’s ideas and their enduring impact on the research community. The book also contains biographical material, Cook’s Turing Award lecture, and an interview. Together these provide a portrait of Cook as a recognized leader and innovator in mathematics and computer science, as well as a gentle mentor and colleague.

Random Walks and Heat Kernels on Graphs

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Publisher : Cambridge University Press
ISBN 13 : 1107674425
Total Pages : 239 pages
Book Rating : 4.1/5 (76 download)

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Book Synopsis Random Walks and Heat Kernels on Graphs by : M. T. Barlow

Download or read book Random Walks and Heat Kernels on Graphs written by M. T. Barlow and published by Cambridge University Press. This book was released on 2017-02-23 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Useful but hard-to-find results enrich this introduction to the analytic study of random walks on infinite graphs.

Mathematical Foundations of Computer Science 2014

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Publisher : Springer
ISBN 13 : 3662444658
Total Pages : 640 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Mathematical Foundations of Computer Science 2014 by : Ersébet Csuhaj-Varjú

Download or read book Mathematical Foundations of Computer Science 2014 written by Ersébet Csuhaj-Varjú and published by Springer. This book was released on 2014-08-12 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two volume set LNCS 8634 and LNCS 8635 constitutes the refereed conference proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014, held in Budapest, Hungary, in August 2014. The 95 revised full papers presented together with 6 invited talks were carefully selected from 270 submissions. The focus of the conference was on following topics: Logic, Semantics, Automata, Theory of Programming, Algorithms, Complexity, Parallel and Distributed Computing, Quantum Computing, Automata, Grammars and Formal Languages, Combinatorics on Words, Trees and Games.

Theory and Applications of Models of Computation

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Publisher : Springer
ISBN 13 : 3540725040
Total Pages : 772 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Theory and Applications of Models of Computation by : Jin-Yi Cai

Download or read book Theory and Applications of Models of Computation written by Jin-Yi Cai and published by Springer. This book was released on 2007-07-23 with total page 772 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 4th International Conference on Theory and Applications of Models of Computation, TAMC 2007, held in Shanghai, China in May 2007. It addresses all major areas in computer science; mathematics, especially logic; and the physical sciences, particularly with regard to computation and computability theory. The papers particularly focus on algorithms, complexity and computability theory.

Surveys in Combinatorics 2017

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Publisher : Cambridge University Press
ISBN 13 : 1108350356
Total Pages : 451 pages
Book Rating : 4.1/5 (83 download)

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Book Synopsis Surveys in Combinatorics 2017 by : Anders Claesson

Download or read book Surveys in Combinatorics 2017 written by Anders Claesson and published by Cambridge University Press. This book was released on 2017-06-30 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: The nine articles in this book represent a timely snapshot of the state of the art in the different areas of combinatorics. They are written by leading experts in the field and provide expanded accounts of plenary seminars given at the British Combinatorial Conference in July 2017.

Polynomials and the mod 2 Steenrod Algebra

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Publisher : Cambridge University Press
ISBN 13 : 1108414451
Total Pages : 381 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Polynomials and the mod 2 Steenrod Algebra by : Grant Walker

Download or read book Polynomials and the mod 2 Steenrod Algebra written by Grant Walker and published by Cambridge University Press. This book was released on 2017-11-09 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second of two volumes covering the Steenrod algebra and its various applications. Ideal for researchers in pure mathematics.

Asymptotic Analysis in General Relativity

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Publisher : Cambridge University Press
ISBN 13 : 1108500781
Total Pages : 381 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Asymptotic Analysis in General Relativity by : Thierry Daudé

Download or read book Asymptotic Analysis in General Relativity written by Thierry Daudé and published by Cambridge University Press. This book was released on 2018-01-11 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume compiles notes from courses given at the summer school on asymptotic analysis in general relativity, held at the Institut Fourier in Grenoble, France. It provides an up-to-date panorama of modern techniques in the asymptotic analysis of classical and quantum fields in general relativity.

Polynomials and the mod 2 Steenrod Algebra: Volume 1, The Peterson Hit Problem

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Publisher : Cambridge University Press
ISBN 13 : 1108355935
Total Pages : 371 pages
Book Rating : 4.1/5 (83 download)

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Book Synopsis Polynomials and the mod 2 Steenrod Algebra: Volume 1, The Peterson Hit Problem by : Grant Walker

Download or read book Polynomials and the mod 2 Steenrod Algebra: Volume 1, The Peterson Hit Problem written by Grant Walker and published by Cambridge University Press. This book was released on 2017-11-09 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This detailed two-volume reference on the Steenrod algebra and its various applications presents more than thirty years of research. Developing the structure of the Steenrod algebra from an algebraic viewpoint, this first volume is recommended for researchers or postgraduates in pure mathematics and can be used as a graduate textbook.

Polynomials and the mod 2 Steenrod Algebra: Volume 2, Representations of GL (n,F2)

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Publisher : Cambridge University Press
ISBN 13 : 1108355927
Total Pages : 381 pages
Book Rating : 4.1/5 (83 download)

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Book Synopsis Polynomials and the mod 2 Steenrod Algebra: Volume 2, Representations of GL (n,F2) by : Grant Walker

Download or read book Polynomials and the mod 2 Steenrod Algebra: Volume 2, Representations of GL (n,F2) written by Grant Walker and published by Cambridge University Press. This book was released on 2017-11-09 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link is provided through a detailed study of Peterson's `hit problem' concerning the action of the Steenrod algebra on polynomials, which remains unsolved except in special cases. The topics range from decompositions of integers as sums of 'powers of 2 minus 1', to Hopf algebras and the Steinberg representation of GL(n, F). Volume 1 develops the structure of the Steenrod algebra from an algebraic viewpoint and can be used as a graduate-level textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.

Dynamics and Analytic Number Theory

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Publisher : Cambridge University Press
ISBN 13 : 1316817776
Total Pages : 341 pages
Book Rating : 4.3/5 (168 download)

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Book Synopsis Dynamics and Analytic Number Theory by : Dzmitry Badziahin

Download or read book Dynamics and Analytic Number Theory written by Dzmitry Badziahin and published by Cambridge University Press. This book was released on 2016-11-10 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by leading experts, this book explores several directions of current research at the interface between dynamics and analytic number theory. Topics include Diophantine approximation, exponential sums, Ramsey theory, ergodic theory and homogeneous dynamics. The origins of this material lie in the 'Dynamics and Analytic Number Theory' Easter School held at Durham University in 2014. Key concepts, cutting-edge results, and modern techniques that play an essential role in contemporary research are presented in a manner accessible to young researchers, including PhD students. This book will also be useful for established mathematicians. The areas discussed include ubiquitous systems and Cantor-type sets in Diophantine approximation, flows on nilmanifolds and their connections with exponential sums, multiple recurrence and Ramsey theory, counting and equidistribution problems in homogeneous dynamics, and applications of thin groups in number theory. Both dynamical and 'classical' approaches towards number theoretical problems are also provided.

Algebraic Combinatorics and the Monster Group

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Publisher : Cambridge University Press
ISBN 13 : 1009338056
Total Pages : 584 pages
Book Rating : 4.0/5 (93 download)

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Book Synopsis Algebraic Combinatorics and the Monster Group by : Alexander A. Ivanov

Download or read book Algebraic Combinatorics and the Monster Group written by Alexander A. Ivanov and published by Cambridge University Press. This book was released on 2023-08-17 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering, arguably, one of the most attractive and mysterious mathematical objects, the Monster group, this text strives to provide an insightful introduction and the discusses the current state of the field. The Monster group is related to many areas of mathematics, as well as physics, from number theory to string theory. This book cuts through the complex nature of the field, highlighting some of the mysteries and intricate relationships involved. Containing many meaningful examples and a manual introduction to the computer package GAP, it provides the opportunity and resources for readers to start their own calculations. Some 20 experts here share their expertise spanning this exciting field, and the resulting volume is ideal for researchers and graduate students working in Combinatorial Algebra, Group theory and related areas.

Modern Trends in Algebra and Representation Theory

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Publisher : Cambridge University Press
ISBN 13 : 1009097350
Total Pages : 407 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Modern Trends in Algebra and Representation Theory by : David Jordan

Download or read book Modern Trends in Algebra and Representation Theory written by David Jordan and published by Cambridge University Press. This book was released on 2023-08-17 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expanding upon the material delivered during the LMS Autumn Algebra School 2020, this volume reflects the fruitful connections between different aspects of representation theory. Each survey article addresses a specific subject from a modern angle, beginning with an exploration of the representation theory of associative algebras, followed by the coverage of important developments in Lie theory in the past two decades, before the final sections introduce the reader to three strikingly different aspects of group theory. Written at a level suitable for graduate students and researchers in related fields, this book provides pure mathematicians with a springboard into the vast and growing literature in each area.