Discrete Mathematics & Theoretical Computer Science

DMTCS

Volume 4 n° 2 (2001), pp. 193-234


author:Martin Müller and Joachim Niehren and Ralf Treinen
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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