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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)

Abstract

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.

Keywords

Normal Form Function Symbol Cover Problem Ground Term Ground Instance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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