Computing ground reducibility and inductively complete positions

  • Reinhard Bündgen
  • Wolfgang Küchlin
Regular Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 355)


We provide the extended ground-reducibility test which is essential for induction with term-rewriting systems based on [Küc89]: Given a term, determine at which sets of positions it is ground-reducible by which subsets of rules. The core of our method is a new parallel cover algorithm based on recursive decomposition. From this we obtain a separation algorithm which determines constructors and defined function symbols in a term-algebra presented by a rewrite system. We then reduce our main problem of extended ground-reducibility to separation and cover. Furthermore, using the knowledge of algebra separation, we refine the bounds of [JK86] for the size of ground reduction test-sets. Both our cover algorithm and our extended ground-reducibility test are engineered to be adaptive to actual problem structure, i.e., to allow for lower than the worst case bounds for test-sets on well conditioned problems, including well conditioned subproblems of difficult cases.


Normal Form Function Symbol Cover Problem Ground Term Ground Instance 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Reinhard Bündgen
    • 1
  • Wolfgang Küchlin
    • 2
  1. 1.Wilhelm-Schickard-InstitutUniversität TübingenTübingenFederal Republic of Germany
  2. 2.Computer and Information SciencesThe Ohio State UniversityColumbusU.S.A.

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