Ehrenfeucht-Fraïssé goes elementarily automatic for structures of bounded degree
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.
Automata-based decision procedures for logical theories
Automatic Structures
Ehrenfeucht-Fraïssé Games
Logics
Complexity
242-253
Regular Paper
Antoine
Durand-Gasselin
Antoine Durand-Gasselin
Peter
Habermehl
Peter Habermehl
10.4230/LIPIcs.STACS.2012.242
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
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