Automatic Structures

  • Authors:
  • Achim Blumensath;Erich Grädel

  • Affiliations:
  • -;-

  • Venue:
  • LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
  • Year:
  • 2000

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Abstract

We study definability and complexity issues for automatic and omega-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 (omega-) 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 characterizations 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.