Complexity of sufficient-completeness

Preliminary version
  • Deepak Kapur
  • Paliath Narendran
  • Hantao Zhang
Session 7 Complexity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 241)


The sufficient-completeness property of equational specifications has been found useful in providing guidelines for abstract data type specifications as well as in proving inductive properties using the inductionless-induction method. The sufficient-completeness property is known to be undecidable in general. In an earlier paper, it was shown to be decidable for constructor-preserving, complete (canonical) term rewriting systems, even when there are relations between constructors. The complexity of the sufficient-completeness property under certain conditions is discussed. It is shown that the sufficient-completeness problem for term rewriting systems without any relations on constructors is co-NP-complete. However, the problem is PSPACE-hard even for linear constructor-preserving term rewriting systems when relations on constructors are allowed.

Key Words

Sufficient-completeness PSPACE term rewriting systems normal forms 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Deepak Kapur
    • 1
  • Paliath Narendran
    • 1
  • Hantao Zhang
    • 2
  1. 1.Corporate Research and DevelopmentGeneral Electric CompanySchenectady
  2. 2.Department of Computer ScienceRensselaer Polytechnic InstituteTroy

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