To Ackermann-ize or not to ackermann-ize? on efficiently handling uninterpreted function symbols in SMT ( ∪T )

  • Authors:

  • Roberto Bruttomesso;Alessandro Cimatti;Anders Franzén;Alberto Griggio;Alessandro Santuari;Roberto Sebastiani

  • Affiliations:

  • ITC-IRST, Povo, Trento, Italy;ITC-IRST, Povo, Trento, Italy;ITC-IRST, Povo, Trento, Italy;DIT, Università di Trento, Italy;DIT, Università di Trento, Italy;DIT, Università di Trento, Italy

  • Venue:
  • LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
  • Year:
  • 2006

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Abstract

Satisfiability Modulo Theories is the problem of deciding the satisfiability of a formula with respect to a given background theory . When is the combination of two simpler theories and , a standard and general approach is to handle the integration of and by performing some form of search on the equalities between the shared variables. A frequent and very relevant sub-case of is when is the theory of Equality and Uninterpreted Functions . For this case, an alternative approach is to eliminate first all uninterpreted function symbols by means of Ackermann's expansion, and then to solve the resulting problem. In this paper we build on the empirical observation that there is no absolute winner between these two alternative approaches, and that the performance gaps between them are often dramatic, in either direction. We propose a simple technique for estimating a priori the costs and benefits, in terms of the size of the search space of an tool, of applying Ackermann's expansion to all or part of the function symbols. A thorough experimental analysis, including the benchmarks of the SMT'05 competition, shows that the proposed technique is extremely effective in improving the overall performance of the tool.