The First-Order Theory of Ground Tree Rewrite Graphs

Göller, Stefan; Lohrey, Markus

doi:10.4230/LIPIcs.FSTTCS.2011.276

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The First-Order Theory of Ground Tree Rewrite Graphs

Authors Stefan Göller, Markus Lohrey

Part of: Volume: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS)
License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
Publication Date: 2011-12-01

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Document Identifiers

DOI: 10.4230/LIPIcs.FSTTCS.2011.276
URN: urn:nbn:de:0030-drops-33220

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Keywords

ground tree rewriting systems
first-order theories
complexity

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Abstract

We prove that the complexity of the uniform first-order theory 
of ground tree rewrite graphs is in ATIME(2^{2^{poly(n)}},O(n).     Providing a matching lower bound, we show that there is some
fixed ground tree rewrite graph whose first-order theory is hard
for ATIME(2^{2^{poly(n)}},poly(n)) with respect to logspace reductions. Finally, we prove that there exists a fixed ground tree rewrite graph together with a single unary predicate in form of a regular tree language such that the resulting structure has a non-elementary first-order theory.

Cite As Get BibTex

Stefan Göller and Markus Lohrey. The First-Order Theory of Ground Tree Rewrite Graphs. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 13, pp. 276-287, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011) https://doi.org/10.4230/LIPIcs.FSTTCS.2011.276

Author Details

Stefan Göller

Markus Lohrey

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