Theories of Automatic Structures and Their Complexity

  • Dietrich Kuske
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5725)


For automatic structures, several logics have been shown decidable: first-order logic, its extension by the infinity quantifier, by modulo-counting quantifiers, and even by a restricted form of second-order quantification. We review these decidability proofs. As a new result, we determine the data, the expression, and the combined complexity of quantifier-classes for first-order logic. Finally, we also recall that first-order logic becomes elementary decidable for automatic structures of bounded degree.


Regular Language Relation Symbol Input Word Bounded Degree Automatic Structure 
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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Dietrich Kuske
    • 1
  1. 1.Institut für InformatikUniversität LeipzigGermany

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