Many approaches for Satisfiability Modulo Theory (
rely on the integration between a SAT solver and a decision procedure for sets of literals in the background theory
is the combination
of two simpler theories, the approach is typically handled by means of Nelson-Oppen’s (NO) theory combination schema in which two specific
deduce and exchange (disjunctions of) interface equalities.
In recent papers we have proposed a new approach to
Delayed Theory Combination
). Here part or all the (possibly very expensive) task of deducing interface equalities is played by the SAT solver itself, at the potential cost of an enlargement of the boolean search space. In principle this enlargement could be up to exponential in the number of interface equalities generated.
In this paper we show that this estimate was too pessimistic. We present a comparative analysis of
vs. NO for
, which shows that, using state-of-the-art SAT-solving techniques, the amount of boolean branches performed by
can be upper bounded by the number of deductions and boolean branches performed by NO on the same problem. We prove the result for different deduction capabilities of the
and for both convex and non-convex theories.