Descriptive Complexity And Finite Models
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Finite Model Theory
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Author : Heinz-Dieter Ebbinghaus
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Finite Model Theory written by Heinz-Dieter Ebbinghaus 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 2013-06-29 with Mathematics categories.
Finite model theory has its origin in classical model theory, but owes its systematic development to research from complexity theory. The book presents the main results of descriptive complexity theory, that is, the connections between axiomatizability of classes of finite structures and their complexity with respect to time and space bounds. The logics that are important in this context include fixed- point logics, transitive closure logics, and also certain infinitary languages; their model theory is studied in full detail. Other topics include DATALOG languages, quantifiers and oracles, 0-1 laws, and optimization and approximation problems. The book is written in such a way that the resp. parts on model theory and descriptive complexity theory may be read independently.
Descriptive Complexity
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Author : Neil Immerman
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-11-20
Descriptive Complexity written by Neil Immerman 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 1998-11-20 with Computers categories.
By virtue of the close relationship between logic and relational databases, it turns out that complexity has important applications to databases such as analyzing the parallel time needed to compute a query, and the analysis of nondeterministic classes. This book is a relatively self-contained introduction to the subject, which includes the necessary background material, as well as numerous examples and exercises.
Finite Model Theory And Its Applications
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Author : Erich Grädel
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-24
Finite Model Theory And Its Applications written by Erich Grädel 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 2007-04-24 with Computers categories.
Finite model theory,as understoodhere, is an areaof mathematicallogic that has developed in close connection with applications to computer science, in particular the theory of computational complexity and database theory. One of the fundamental insights of mathematical logic is that our understanding of mathematical phenomena is enriched by elevating the languages we use to describe mathematical structures to objects of explicit study. If mathematics is the science of patterns, then the media through which we discern patterns, as well as the structures in which we discern them, command our attention. It isthis aspect oflogicwhichis mostprominentin model theory,“thebranchof mathematical logic which deals with the relation between a formal language and its interpretations”. No wonder, then, that mathematical logic, and ?nite model theory in particular, should ?nd manifold applications in computer science: from specifying programs to querying databases, computer science is rife with phenomena whose understanding requires close attention to the interaction between language and structure. This volume gives a broadoverviewof some central themes of ?nite model theory: expressive power, descriptive complexity, and zero–one laws, together with selected applications to database theory and arti?cial intelligence, es- cially constraint databases and constraint satisfaction problems. The ?nal chapter provides a concise modern introduction to modal logic,which emp- sizes the continuity in spirit and technique with ?nite model theory.
Descriptive Complexity And Finite Models
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Author : Neil Immerman
language : en
Publisher: American Mathematical Soc.
Release Date : 1997-01-01
Descriptive Complexity And Finite Models written by Neil Immerman 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 1997-01-01 with Computers categories.
This volume presents articles by leading researchers who delivered talks at the "Workshop on Finite Models and Descriptive Complexity" at Princeton in January 1996 during a DIMACS sponsored Special Year on Logic and Algorithms. Each article is self-contained and provides a valuable introduction to the featured research areas connected with finite model theory.
Descriptive Complexity And Finite Models
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Author : Neil Immerman
language : en
Publisher:
Release Date : 1997
Descriptive Complexity And Finite Models written by Neil Immerman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Computational complexity categories.
"We hope that this small volume will suggest directions of synergy and contact for future researchers to build upon, creating connections and making discoveries that will help explain some of the many mysteries of computation."--The Preface Finite model theory can be succinctly described as the study of logics on finite structures. It is an area of research existing between mathematical logic and computer science. This area has been developing through continuous interaction with computational complexity, database theory, and combinatorics. The volume presents articles by leading researche.
Descriptive Set Theoretic Methods In Automata Theory
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Author : Michał Skrzypczak
language : en
Publisher: Springer
Release Date : 2016-08-05
Descriptive Set Theoretic Methods In Automata Theory written by Michał Skrzypczak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-05 with Mathematics categories.
The book is based on the PhD thesis “Descriptive Set Theoretic Methods in Automata Theory,” awarded the E.W. Beth Prize in 2015 for outstanding dissertations in the fields of logic, language, and information. The thesis reveals unexpected connections between advanced concepts in logic, descriptive set theory, topology, and automata theory and provides many deep insights into the interplay between these fields. It opens new perspectives on central problems in the theory of automata on infinite words and trees and offers very impressive advances in this theory from the point of view of topology. "...the thesis of Michał Skrzypczak offers certainly what we expect from excellent mathematics: new unexpected connections between a priori distinct concepts, and proofs involving enlightening ideas.” Thomas Colcombet.
The Classical Decision Problem
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Author : Egon Börger
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-08-28
The Classical Decision Problem written by Egon Börger 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 2001-08-28 with Mathematics categories.
This book offers a comprehensive treatment of the classical decision problem of mathematical logic and of the role of the classical decision problem in modern computer science. The text presents a revealing analysis of the natural order of decidable and undecidable cases and includes a number of simple proofs and exercises.
Complexity Of Infinite Domain Constraint Satisfaction
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Author : Manuel Bodirsky
language : en
Publisher: Cambridge University Press
Release Date : 2021-06-10
Complexity Of Infinite Domain Constraint Satisfaction written by Manuel Bodirsky 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 2021-06-10 with Mathematics categories.
Constraint Satisfaction Problems (CSPs) are natural computational problems that appear in many areas of theoretical computer science. Exploring which CSPs are solvable in polynomial time and which are NP-hard reveals a surprising link with central questions in universal algebra. This monograph presents a self-contained introduction to the universal-algebraic approach to complexity classification, treating both finite and infinite-domain CSPs. It includes the required background from logic and combinatorics, particularly model theory and Ramsey theory, and explains the recently discovered link between Ramsey theory and topological dynamics and its implications for CSPs. The book will be of interest to graduate students and researchers in theoretical computer science and to mathematicians in logic, combinatorics, and dynamics who wish to learn about the applications of their work in complexity theory.
Finite Model Theory And Its Applications
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Author : Erich Grädel
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-04
Finite Model Theory And Its Applications written by Erich Grädel 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 2007-06-04 with Computers categories.
Finite model theory,as understoodhere, is an areaof mathematicallogic that has developed in close connection with applications to computer science, in particular the theory of computational complexity and database theory. One of the fundamental insights of mathematical logic is that our understanding of mathematical phenomena is enriched by elevating the languages we use to describe mathematical structures to objects of explicit study. If mathematics is the science of patterns, then the media through which we discern patterns, as well as the structures in which we discern them, command our attention. It isthis aspect oflogicwhichis mostprominentin model theory,“thebranchof mathematical logic which deals with the relation between a formal language and its interpretations”. No wonder, then, that mathematical logic, and ?nite model theory in particular, should ?nd manifold applications in computer science: from specifying programs to querying databases, computer science is rife with phenomena whose understanding requires close attention to the interaction between language and structure. This volume gives a broadoverviewof some central themes of ?nite model theory: expressive power, descriptive complexity, and zero–one laws, together with selected applications to database theory and arti?cial intelligence, es- cially constraint databases and constraint satisfaction problems. The ?nal chapter provides a concise modern introduction to modal logic,which emp- sizes the continuity in spirit and technique with ?nite model theory.
Descriptive Complexity Canonisation And Definable Graph Structure Theory
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Author : Martin Grohe
language : en
Publisher: Cambridge University Press
Release Date : 2017-08-17
Descriptive Complexity Canonisation And Definable Graph Structure Theory written by Martin Grohe 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 2017-08-17 with Computers categories.
This groundbreaking, yet accessible book explores the interaction between graph theory and computational complexity using methods from finite model theory.