Simple and Minimal Ground Term Equation Systems

  • Authors:

  • Sándor Vágvölgyi

  • Affiliations:

  • (Correspd.) Department of Applied Informatics, József Attila University, Szeged, Árpád tér 2, H-6720 Hungary. e-mail:vagvolgy@inf.u-szeged.hu

  • Venue:
  • Fundamenta Informaticae
  • Year:
  • 1998

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Abstract

A ground term equation system (gtes for short) E is simple if there is no gtes E′ equivalent to E consisting of less equations than E has. Moreover, a gtes E is minimal if for each equation e ∈ E, the congruence generated by E - {e} is a proper subset of the congruence generated by E. Given a reduced ground term rewriting system R, we describe all simple gtes' E and minimal gtes' F equivalent to R. We show that for a reduced ground term rewriting system R, it is decidable whether or not there exist infinitely many simple (minimal) gtes' equivalent to R. Finally, we show that for a reduced ground term rewriting system R, and a gtes E, it is decidable if there is a simple gtes F equivalent to R such that E ⊆ F.