The Con uence of Ground Term RewriteSystems is Decidable in Polynomial

Abstract

The connuence property of ground (i.e., variable-free) term rewrite systems (GTRS) is well-known to be decidable. This was proved independently in DTHL87,DHLT90] and in Oya87] using tree automata techniques and ground tree transducer techniques (originated from this problem), yielding EXPTIME decision procedures (PSPACE for strings). Since then, it has been a well-known longstanding open question whether this bound is optimal (see, e.g., RTA01]). Here we give a polynomial-time algorithm for deciding the connuence of GTRS, and hence as well for the particular case of suux-and preex string rewrite systems or Thue systems. We show that this bound is optimal for all these problems by proving PTIME-hardness for the string case. This result may have some impact as well on other areas of formal language theory and, in particular, on the theory of tree automata.

Cite this paper

@inproceedings{Comon2001TheCU, title={The Con uence of Ground Term RewriteSystems is Decidable in Polynomial}, author={Hubert Comon and Guillem Godoy and Robert Nieuwenhuis}, year={2001} }