Paper: The First-Order Theory of Ordering Constraints over Feature Trees (at LICS 1998)

Authors: Martin Müller Joachim Niehren Ralf Treinen

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, 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 determine the complexity of the entailment problem of FT_⩽ with existential quantification to be PSPACE-complete, by proving its equivalence to the inclusion problem of non-deterministic finite automata. Our reduction from the entailment problem to the inclusion problem is based on a new algorithm that, given an existential formula of FT_⩽, computes a finite automaton which accepts all its logic consequences

BibTeX

  @InProceedings{MllerNiehrenTreinen-TheFirstOrderTheory,
    author = 	 {Martin Müller and Joachim Niehren and Ralf Treinen},
    title = 	 {The First-Order Theory of Ordering Constraints over Feature Trees},
    booktitle =  {Proceedings of the Thirteenth Annual IEEE Symposium on Logic in Computer Science (LICS 1998)},
    year =	 {1998},
    month =	 {June}, 
    pages =      {432--443},
    location =   {Indianapolis, IN, USA}, 
    publisher =	 {IEEE Computer Society Press}
  }