Finite Model Theory
First Edition
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Beschreibung
Finite model theory has its origins 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 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.
The branch of model theory described in the present book and called finite model theory has its roots in classical model theory but owes its systematic development to research from complexity theory. For the first time in book form, the authors provide a comprehensive presentation of the main results in this field. The book addresses logicians and computer scientists.
Autor*in
Heinz-Dieter Ebbinghaus
Themen in »Finite Model Theory«
0-1-Gesetze 0-1-laws Deskriptive Komplexitätstheorie Fixpunktlogiken automata boolean satisfiability problem complexity complexity theory description complexity theory finite model theory fixed-point logics logic model theory optimization theory of complexity
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"..a concise exposition that is at the same time comprehensive and lucid, providing good motivations and clear examples. The book can be thoroughly recommended for self-study and reference, or for an advanced course on this vital new subject." New Zealand Mathematical Society Newsletter
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