Finite And Algorithmic Model Theory
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Finite And Algorithmic Model Theory
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Author : Javier Esparza
language : en
Publisher: Cambridge University Press
Release Date : 2011-03-10
Finite And Algorithmic Model Theory written by Javier Esparza 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 2011-03-10 with Computers categories.
Surveys of current research in logical aspects of computer science that apply finite and infinite model-theoretic methods.
Finite Model Theory
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Author : Heinz-Dieter Ebbinghaus
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-29
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 2005-12-29 with Mathematics categories.
Finite model theory, the model theory of finite structures, has roots in clas sical model theory; however, its systematic development was strongly influ enced by research and questions of complexity theory and of database theory. Model theory or the theory of models, as it was first named by Tarski in 1954, may be considered as the part of the semantics of formalized languages that is concerned with the interplay between the syntactic structure of an axiom system on the one hand and (algebraic, settheoretic, . . . ) properties of its models on the other hand. As it turned out, first-order language (we mostly speak of first-order logic) became the most prominent language in this respect, the reason being that it obeys some fundamental principles such as the compactness theorem and the completeness theorem. These principles are valuable modeltheoretic tools and, at the same time, reflect the expressive weakness of first-order logic. This weakness is the breeding ground for the freedomwhich modeltheoretic methods rest upon. By compactness, any first-order axiom system either has only finite models of limited cardinality or has infinite models. The first case is trivial because finitely many finite structures can explicitly be described by a first-order sentence. As model theory usually considers all models of an axiom system, modeltheorists were thus led to the second case, that is, to infinite structures. In fact, classical model theory of first-order logic and its generalizations to stronger languages live in the realm of the infinite.
Finite And Algorithmic Model Theory
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Author : Javier Esparza
language : en
Publisher:
Release Date : 2014-05-14
Finite And Algorithmic Model Theory written by Javier Esparza and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Computer science categories.
Surveys of current research in logical aspects of computer science that apply finite and infinite model-theoretic methods.
Finite Model Theory
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Author : Heinz-Dieter Ebbinghaus
language : en
Publisher: Springer
Release Date : 2014-03-12
Finite Model Theory written by Heinz-Dieter Ebbinghaus and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-12 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.
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.
Finite Markov Chains And Algorithmic Applications
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Author : Olle Häggström
language : en
Publisher: Cambridge University Press
Release Date : 2002-05-30
Finite Markov Chains And Algorithmic Applications written by Olle Häggström 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 2002-05-30 with Mathematics categories.
Based on a lecture course given at Chalmers University of Technology, this 2002 book is ideal for advanced undergraduate or beginning graduate students. The author first develops the necessary background in probability theory and Markov chains before applying it to study a range of randomized algorithms with important applications in optimization and other problems in computing. Amongst the algorithms covered are the Markov chain Monte Carlo method, simulated annealing, and the recent Propp-Wilson algorithm. This book will appeal not only to mathematicians, but also to students of statistics and computer science. The subject matter is introduced in a clear and concise fashion and the numerous exercises included will help students to deepen their understanding.
Effective Results And Methods For Diophantine Equations Over Finitely Generated Domains
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Author : Jan-Hendrik Evertse
language : en
Publisher: Cambridge University Press
Release Date : 2022-04-28
Effective Results And Methods For Diophantine Equations Over Finitely Generated Domains written by Jan-Hendrik Evertse 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 2022-04-28 with Mathematics categories.
Provides exceptional coverage of effective solutions for Diophantine equations over finitely generated domains.
The Logical Approach To Automatic Sequences
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Author : Jeffrey Shallit
language : en
Publisher: Cambridge University Press
Release Date : 2022-09-29
The Logical Approach To Automatic Sequences written by Jeffrey Shallit 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 2022-09-29 with Computers categories.
Automatic sequences are sequences over a finite alphabet generated by a finite-state machine. This book presents a novel viewpoint on automatic sequences, and more generally on combinatorics on words, by introducing a decision method through which many new results in combinatorics and number theory can be automatically proved or disproved with little or no human intervention. This approach to proving theorems is extremely powerful, allowing long and error-prone case-based arguments to be replaced by simple computations. Readers will learn how to phrase their desired results in first-order logic, using free software to automate the computation process. Results that normally require multipage proofs can emerge in milliseconds, allowing users to engage with mathematical questions that would otherwise be difficult to solve. With more than 150 exercises included, this text is an ideal resource for researchers, graduate students, and advanced undergraduates studying combinatorics, sequences, and number theory.
Geometry Topology And Dynamics In Negative Curvature
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Author : C. S. Aravinda
language : en
Publisher: Cambridge University Press
Release Date : 2016-01-21
Geometry Topology And Dynamics In Negative Curvature written by C. S. Aravinda 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 2016-01-21 with Mathematics categories.
Ten high-quality survey articles provide an overview of important recent developments in the mathematics surrounding negative curvature.
Co End Calculus
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Author : Fosco Loregian
language : en
Publisher: Cambridge University Press
Release Date : 2021-07-22
Co End Calculus written by Fosco Loregian 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 2021-07-22 with Mathematics categories.
This easy-to-cite handbook gives the first systematic treatment of the (co)end calculus in category theory and its applications.