Satisfiability Modulo Theories
is the problem of deciding the satisfiability of a formula with respect to a given background theory
is the combination of two simpler theories
, a standard and general approach is to handle the integration of
by performing some form of search on the equalities between the shared variables.
A frequent and very relevant sub-case of
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
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