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Finite Model Theory
ISBN-13:
9783540287889
Veröffentl:
2005
Seiten:
360
Autor:
Heinz-Dieter Ebbinghaus
Serie:
Springer Monographs in Mathematics
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
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.
"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 respective parts on model theory and descriptive complexity theory may be read independently. This second edition is a thoroughly revised and enlarged version of the original text."
Preliminaries.- The Ehrenfeucht-Fraïssé Method.- More on Games.- 0-1 Laws.- Satisfiability in the Finite.- Finite Automata and Logic: A Microcosm of Finite Model Theory.- Descriptive Complexity Theory.- Logics with Fixed-Point Operators.- Logic Programs.- Optimization Problems.- Logics for PTIME.- Quantifiers and Logical Reductions.
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