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

Source : oai:HAL:inria-00536800v1

Volume: Vol. 4 no. 2

Published on: January 1, 2001

Submitted on: March 26, 2015

Keywords: [INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO],[INFO.INFO-FL] Computer Science [cs]/Formal Languages and Automata Theory [cs.FL]

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