A Randomized Satisfiability Procedure for Arithmetic and Uninterpreted Function Symbols

  • Sumit Gulwani
  • George C. Necula
Conference paper

DOI: 10.1007/978-3-540-45085-6_14

Volume 2741 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Gulwani S., Necula G.C. (2003) A Randomized Satisfiability Procedure for Arithmetic and Uninterpreted Function Symbols. In: Baader F. (eds) Automated Deduction – CADE-19. CADE 2003. Lecture Notes in Computer Science, vol 2741. Springer, Berlin, Heidelberg

Abstract

We present a new randomized algorithm for checking the satisfiability of a conjunction of literals in the combined theory of linear equalities and uninterpreted functions. The key idea of the algorithm is to process the literals incrementally and to maintain at all times a set of random variable assignments that satisfy the literals seen so far. We prove that this algorithm is complete (i.e., it identifies all unsatisfiable conjunctions) and is probabilistically sound (i.e., the probability that it fails to identify satisfiable conjunctions is very small). The algorithm has the ability to retract assumptions incrementally with almost no additional space overhead. The key advantage of the algorithm is its simplicity. We also show experimentally that the randomized algorithm has performance competitive with the existing deterministic symbolic algorithms.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Sumit Gulwani
    • 1
  • George C. Necula
    • 1
  1. 1.University of CaliforniaBerkeley