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Descriptive Complexity And Finite Models
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Book Synopsis Descriptive Complexity and Finite Models by : Neil Immerman
Download or read book Descriptive Complexity and Finite Models written by Neil Immerman and published by American Mathematical Soc.. This book was released on 1997 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Preface: 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. 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 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. This text will also be of interest to those working in discrete mathematics and combinatorics.
Book Synopsis Descriptive Complexity by : Neil Immerman
Download or read book Descriptive Complexity written by Neil Immerman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author :Heinz-Dieter Ebbinghaus Publisher :Springer Science & Business Media ISBN 13 :3540287884 Total Pages :363 pages Book Rating :4.5/5 (42 download)
Book Synopsis Finite Model Theory by : Heinz-Dieter Ebbinghaus
Download or read book Finite Model Theory written by Heinz-Dieter Ebbinghaus and published by Springer Science & Business Media. This book was released on 2005-12-29 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a thoroughly revised and enlarged second edition that 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. The book is written in such a way that the respective parts on model theory and descriptive complexity theory may be read independently.
Book Synopsis Elements of Finite Model Theory by : Leonid Libkin
Download or read book Elements of Finite Model Theory written by Leonid Libkin and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizes the computer science aspects of the subject. Details applications in databases, complexity theory, and formal languages, as well as other branches of computer science.
Author :Heinz-Dieter Ebbinghaus Publisher :Springer Science & Business Media ISBN 13 :3662031825 Total Pages :336 pages Book Rating :4.6/5 (62 download)
Book Synopsis Finite Model Theory by : Heinz-Dieter Ebbinghaus
Download or read book Finite Model Theory written by Heinz-Dieter Ebbinghaus and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Finite Model Theory and Its Applications by : Erich Grädel
Download or read book Finite Model Theory and Its Applications written by Erich Grädel and published by Springer Science & Business Media. This book was released on 2007-06-04 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Finite Model Theory by : Heinz-Dieter Ebbinghaus
Download or read book Finite Model Theory written by Heinz-Dieter Ebbinghaus and published by Springer. This book was released on 2014-03-12 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Finite and Algorithmic Model Theory by : Javier Esparza
Download or read book Finite and Algorithmic Model Theory written by Javier Esparza and published by Cambridge University Press. This book was released on 2011-03-10 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveys of current research in logical aspects of computer science that apply finite and infinite model-theoretic methods.
Book Synopsis Bounded Variable Logics and Counting by : Martin Otto
Download or read book Bounded Variable Logics and Counting written by Martin Otto and published by Cambridge University Press. This book was released on 2017-03-02 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study introduces some central ideas and lines of research in finite model theory - particularly bounded variable infinitary logics - and explores the fruitful exchange between ideas from logic and from complexity theory that is characteristic of finite model theory.
Book Synopsis Computational Complexity by : Sanjeev Arora
Download or read book Computational Complexity written by Sanjeev Arora and published by Cambridge University Press. This book was released on 2009-04-20 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Book Synopsis An Introduction to Kolmogorov Complexity and Its Applications by : Ming Li
Download or read book An Introduction to Kolmogorov Complexity and Its Applications written by Ming Li and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo rithmic complexity theory. The theory of Martin-Lof tests for random ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).
Book Synopsis A First Course in Logic by : Shawn Hedman
Download or read book A First Course in Logic written by Shawn Hedman and published by OUP Oxford. This book was released on 2004-07-08 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, this text covers the fundamental topics in classical logic in an extremely clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, and model theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course.
Book Synopsis Handbook of Finite State Based Models and Applications by : Jiacun Wang
Download or read book Handbook of Finite State Based Models and Applications written by Jiacun Wang and published by CRC Press. This book was released on 2016-04-19 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applicable to any problem that requires a finite number of solutions, finite state-based models (also called finite state machines or finite state automata) have found wide use in various areas of computer science and engineering. Handbook of Finite State Based Models and Applications provides a complete collection of introductory materials on fini
Book Synopsis Complexity of Infinite-Domain Constraint Satisfaction by : Manuel Bodirsky
Download or read book Complexity of Infinite-Domain Constraint Satisfaction written by Manuel Bodirsky and published by Cambridge University Press. This book was released on 2021-06-10 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces the universal-algebraic approach to classifying the computational complexity of constraint satisfaction problems.
Book Synopsis Descriptive Complexity, Canonisation, and Definable Graph Structure Theory by : Martin Grohe
Download or read book Descriptive Complexity, Canonisation, and Definable Graph Structure Theory written by Martin Grohe and published by Cambridge University Press. This book was released on 2017-08-17 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: This groundbreaking, yet accessible book explores the interaction between graph theory and computational complexity using methods from finite model theory.
Book Synopsis Finite Model Theory and Its Applications by : Erich Grädel
Download or read book Finite Model Theory and Its Applications written by Erich Grädel and published by Springer Science & Business Media. This book was released on 2007-04-24 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Descriptive Complexity, Canonisation, and Definable Graph Structure Theory by : Martin Grohe
Download or read book Descriptive Complexity, Canonisation, and Definable Graph Structure Theory written by Martin Grohe and published by Cambridge University Press. This book was released on 2017-08-17 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Descriptive complexity theory establishes a connection between the computational complexity of algorithmic problems (the computational resources required to solve the problems) and their descriptive complexity (the language resources required to describe the problems). This groundbreaking book approaches descriptive complexity from the angle of modern structural graph theory, specifically graph minor theory. It develops a 'definable structure theory' concerned with the logical definability of graph theoretic concepts such as tree decompositions and embeddings. The first part starts with an introduction to the background, from logic, complexity, and graph theory, and develops the theory up to first applications in descriptive complexity theory and graph isomorphism testing. It may serve as the basis for a graduate-level course. The second part is more advanced and mainly devoted to the proof of a single, previously unpublished theorem: properties of graphs with excluded minors are decidable in polynomial time if, and only if, they are definable in fixed-point logic with counting.
