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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2001

The First-Order Theory of Ordering Constraints over Feature Trees

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. Available at http://www.ps.uni-saarland.de/Publications/documents/FTSubTheory_98.pdf
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Dates and versions

inria-00536800 , version 1 (11-06-2014)

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Martin Müller, Joachim Niehren, Ralf Treinen. The First-Order Theory of Ordering Constraints over Feature Trees. Discrete Mathematics and Theoretical Computer Science, 2001, Vol. 4 no. 2 (2), pp.193-234. ⟨10.46298/dmtcs.267⟩. ⟨inria-00536800⟩
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