Join Algorithms for the Theory of Uninterpreted Functions

  • Sumit Gulwani
  • Ashish Tiwari
  • George C. Necula
Conference paper

DOI: 10.1007/978-3-540-30538-5_26

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3328)
Cite this paper as:
Gulwani S., Tiwari A., Necula G.C. (2004) Join Algorithms for the Theory of Uninterpreted Functions. In: Lodaya K., Mahajan M. (eds) FSTTCS 2004: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2004. Lecture Notes in Computer Science, vol 3328. Springer, Berlin, Heidelberg

Abstract

The join of two sets of facts, E1 and E2, is defined as the set of all facts that are implied independently by both E1 and E2. Congruence closure is a widely used representation for sets of equational facts in the theory of uninterpreted function symbols (UFS). We present an optimal join algorithm for special classes of the theory of UFS using the abstract congruence closure framework. Several known join algorithms, which work on a strict subclass, can be cast as specific instantiations of our generic procedure. We demonstrate the limitations of any approach for computing joins that is based on the use of congruence closure. We also mention some interesting open problems in this area.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Sumit Gulwani
    • 1
  • Ashish Tiwari
    • 2
  • George C. Necula
    • 1
  1. 1.University of CaliforniaBerkeley
  2. 2.SRI InternationalMenlo Park

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