Congruence closure of compressed terms in polynomial time

  • Authors:

  • Manfred Schmidt-Schauss;David Sabel;Altug Anis

  • Affiliations:

  • Dept. Informatik und Mathematik, Inst. Informatik, Goethe-University, Frankfurt, Germany;Dept. Informatik und Mathematik, Inst. Informatik, Goethe-University, Frankfurt, Germany;Dept. Informatik und Mathematik, Inst. Informatik, Goethe-University, Frankfurt, Germany

  • Venue:
  • FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
  • Year:
  • 2011

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Abstract

The word-problem for a finite set of equational axioms between ground terms is the question whether for terms s, t the equation s = t is a consequence. We consider this problem under grammar based compression of terms, in particular compression with singleton tree grammars (STGs) and with directed acyclic graphs (DAGs) as a special case. We show that given a DAG-compressed ground and reduced term rewriting system T, the T-normal form of an STG-compressed term s can be computed in polynomial time, and hence the T-word problem can be solved in polynomial time. This implies that the word problem of STG-compressed terms w.r.t. a set of DAG-compressed ground equations can be decided in polynomial time. If the ground term rewriting system (gTRS) T is STG-compressed, we show NP-hardness of T-normal-form computation. For compressed, reduced gTRSs we show a PSPACE upper bound on the complexity of the normal form computation of STG-compressed terms. Also special cases are considered and a prototypical implementation is presented.