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Automatic structures

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2 Author(s)
Blumensath, A. ; Math. Grundlagen der Inf., Tech. Hochschule Aachen, Germany ; Gradel, E.

We study definability and complexity issues for automatic and ω-automatic structures. These are, in general, infinite structures but they can be finitely presented by a collection of automata. Moreover they admit effective (in fact automatic) evaluation of all first-order queries. Therefore, automatic structures provide an interesting framework for extending many algorithmic and logical methods from finite structures to infinite ones. We explain the notion of (ω-)automatic structures, give examples, and discuss the relationship to automatic groups. We determine the complexity of model checking and query evaluation on automatic structures for fragments of first-order logic. Further we study closure properties and definability issues on automatic structures and present a technique for proving that a structure is not automatic. We give model-theoretic characterisations for automatic structures via interpretations. Finally we discuss the composition theory of automatic structures and prove that they are closed under finitary Feferman-Vaught-like products

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Logic in Computer Science, 2000. Proceedings. 15th Annual IEEE Symposium on

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