Adapting Real Quantifier Elimination Methods for Conflict Set Computation

Abstract

International audienceThe satisfiability problem in real closed fields is decidable. In the context of satisfiability modulo theories, the problem restricted to conjunctive sets of literals, that is, sets of polynomial constraints, is of particular importance. One of the central problems is the computation of good explanations of the unsatisfiability of such sets, i.e. obtaining a small subset of the input constraints whose conjunction is already unsatisfiable. We adapt two commonly used real quantifier elimination methods, cylindrical algebraic decomposition and virtual substitution, to provide such conflict sets and demonstrate the performance of our method in practice

Deciding the Consistency of Non-Linear Real Arithmetic Constraints with a Conflict Driven Search Using Cylindrical Algebraic Coverings

“…For now we simply make the reasonable assumption of the existence of an algorithm compute cover which computes such a good covering of the real line as a subset of an existing covering I. Since it is not crucial we will not specify the algorithm here, but we note that the ideas in [37] may be useful.…”