Descriptive Complexity And Finite Models
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Author | : Neil Immerman |
Publisher | : Springer Science & Business Media |
Total Pages | : 275 |
Release | : 2012-12-06 |
Genre | : Computers |
ISBN | : 1461205395 |
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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 | : Neil Immerman |
Publisher | : American Mathematical Soc. |
Total Pages | : 265 |
Release | : 1997 |
Genre | : Computers |
ISBN | : 0821805177 |
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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.
Author | : Leonid Libkin |
Publisher | : Springer Science & Business Media |
Total Pages | : 320 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 3662070030 |
Download Elements of Finite Model Theory Book in PDF, Epub and Kindle
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 |
Total Pages | : 363 |
Release | : 2005-12-29 |
Genre | : Mathematics |
ISBN | : 3540287884 |
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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.
Author | : Heinz-Dieter Ebbinghaus |
Publisher | : Springer Science & Business Media |
Total Pages | : 336 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 3662031825 |
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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.
Author | : Heinz-Dieter Ebbinghaus |
Publisher | : Springer |
Total Pages | : 327 |
Release | : 2014-03-12 |
Genre | : Mathematics |
ISBN | : 9783662031834 |
Download Finite Model Theory Book in PDF, Epub and Kindle
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.
Author | : Erich Grädel |
Publisher | : Springer Science & Business Media |
Total Pages | : 447 |
Release | : 2007-06-04 |
Genre | : Computers |
ISBN | : 3540688048 |
Download Finite Model Theory and Its Applications Book in PDF, Epub and Kindle
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.
Author | : Martin Otto |
Publisher | : Springer |
Total Pages | : 208 |
Release | : 1997-01-28 |
Genre | : Computers |
ISBN | : |
Download Bounded Variable Logics and Counting Book in PDF, Epub and Kindle
This monograph in finite model theory offers a comprehensive treatment of a variety of results in the model theory and descriptive complexity theory of infinitary logics with a bounded number of variables and logics with counting constructs. The exposition is largely self-contained, with introductory sections on the relevant logics, model theoretic concepts, and the programme of descriptive complexity.
Author | : Javier Esparza |
Publisher | : Cambridge University Press |
Total Pages | : 355 |
Release | : 2011-03-10 |
Genre | : Computers |
ISBN | : 0521718201 |
Download Finite and Algorithmic Model Theory Book in PDF, Epub and Kindle
Surveys of current research in logical aspects of computer science that apply finite and infinite model-theoretic methods.
Author | : Martin Grohe |
Publisher | : Cambridge University Press |
Total Pages | : 554 |
Release | : 2017-08-17 |
Genre | : Computers |
ISBN | : 1107014522 |
Download Descriptive Complexity, Canonisation, and Definable Graph Structure Theory Book in PDF, Epub and Kindle
This groundbreaking, yet accessible book explores the interaction between graph theory and computational complexity using methods from finite model theory.