## About this book

### Introduction

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.

### Keywords

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

#### Authors and affiliations

- Heinz-Dieter Ebbinghaus
- Jörg Flum

- 1.Institute of Mathematical LogicUniversity of FreiburgFreiburgGermany

### Bibliographic information