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Ehrenfeucht-Fraïssé goes elementarily automatic for structures of bounded degree

Authors Antoine Durand-Gasselin, Peter Habermehl



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LIPIcs.STACS.2012.242.pdf
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Antoine Durand-Gasselin
Peter Habermehl

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Antoine Durand-Gasselin and Peter Habermehl. Ehrenfeucht-Fraïssé goes elementarily automatic for structures of bounded degree. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 242-253, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)
https://doi.org/10.4230/LIPIcs.STACS.2012.242

Abstract

Many relational structures are automatically presentable, i.e. elements of the domain can be seen as words over a finite alphabet and equality and other atomic relations are represented with finite automata. The first-order theories over such structures are known to be primitive recursive, which is shown by the inductive construction of an automaton representing any relation definable in the first-order logic. We propose a general method based on Ehrenfeucht-Fraïssé games to give upper bounds on the size of these automata and on the time required to build them. We apply this method for two different automatic structures which have elementary decision procedures, Presburger Arithmetic and automatic structures of bounded degree. For the latter no upper bound on the size of the automata was known. We conclude that the very general and simple automata-based algorithm works well to decide the first-order theories over these structures.
Keywords
  • Automata-based decision procedures for logical theories
  • Automatic Structures
  • Ehrenfeucht-Fraïssé Games
  • Logics
  • Complexity

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