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Automatic structures of bounded degree revisited

Published online by Cambridge University Press:  12 March 2014

Dietrich Kuske  and
Markus Lohrey
Dietrich Kuske
Affiliation:
Technische Universität Ilmenau, Institut für Theoretische Informatik, Ilmenau, Germany, E-mail: dietrich.kuske@tu-ilmenau.de
Markus Lohrey
Affiliation:
Universität Leipzig, Institut für Informatik, Leipzig, Germany, E-mail: lohrey@informatik.uni-leipzig.de
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Abstract

The first-order theory of a string automatic structure is known to be decidable, but there are examples of string automatic structures with nonelementary first-order theories. We prove that the first-order theory of a string automatic structure of bounded degree is decidable in doubly exponential space (for injective automatic presentations, this holds even uniformly). This result is shown to be optimal since we also present a string automatic structure of bounded degree whose first-order theory is hard for 2EXPSPACE. We prove similar results also for tree automatic structures. These findings close the gaps left open in [28] by improving both the lower and the upper bounds.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 4 , December 2011 , pp. 1352 - 1380
Copyright
Copyright © Association for Symbolic Logic 2011

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