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December 2011 Automatic structures of bounded degree revisited
Dietrich Kuske, Markus Lohrey
J. Symbolic Logic 76(4): 1352-1380 (December 2011). DOI: 10.2178/jsl/1318338854

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.

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Dietrich Kuske. Markus Lohrey. "Automatic structures of bounded degree revisited." J. Symbolic Logic 76 (4) 1352 - 1380, December 2011. https://doi.org/10.2178/jsl/1318338854

Information

Published: December 2011
First available in Project Euclid: 11 October 2011

zbMATH: 1272.03148
MathSciNet: MR2895400
Digital Object Identifier: 10.2178/jsl/1318338854

Rights: Copyright © 2011 Association for Symbolic Logic

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Vol.76 • No. 4 • December 2011
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