Discrete Mathematics & Theoretical Computer Science
Volume 4 n° 2 (2001), pp. 193-234
author: | Martin Müller and Joachim Niehren and Ralf Treinen |
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title: | The first-order theory of ordering constraints over feature trees |
keywords: | feature constraints, logic of trees, automata |
abstract: | The system FT_{≤} of ordering constraints over feature trees has been introduced as an extension of the system FT of equality constraints over feature trees. We investigate the first-order theory of FT_{≤} and its fragments in detail, both over finite trees and over possibly infinite trees. We prove that the first-order theory of FT_{≤} is undecidable, in contrast to the first-order theory of FT which is well-known to be decidable. We show that the entailment problem of FT_{≤} with existential quantification is PSPACE-complete. So far, this problem has been shown decidable, coNP-hard in case of finite trees, PSPACE-hard in case of arbitrary trees, and cubic time when restricted to quantifier-free entailment judgments. To show PSPACE-completeness, we show that the entailment problem of FT_{≤} with existential quantification is equivalent to the inclusion problem of non-deterministic finite automata. |
reference: | Martin Müller and Joachim Niehren and Ralf Treinen (2001), The first-order theory of ordering constraints over feature trees , Discrete Mathematics and Theoretical Computer Science 4, pp. 193-234 |
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Automatically produced on Thu Sep 13 21:57:56 CEST 2001 by ifalk