Evaluation of Equational Constraints for CAD in SMT Solving

The cylindrical algebraic decomposition algorithm is a quantifier elimination method for real-algebraic formulae. We use it as a theory solver in the context of satisfiability-modulo-theories (SMT) solving to solve sequences of related real-algebraic satisfiability questions. In this paper, we consider some optimizations for handling equational constraints. We review some previously published ideas, in particular Brown’s projection operator and some improvements suggested by McCallum. Then we discuss different variants of the restricted projection operator to implement them in our SMT solver SMT-RAT and provide experimental results on the SMT-LIB benchmark set QF NRA. We show that the performance improves especially for unsatisfiable inputs.

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