QSMA: A New Algorithm for Quantified Satisfiability Modulo Theory and Assignment

Abstract

This paper presents and proves totally correct a new algorithm, called $$\textsf{QSMA}$$ QSMA , for the satisfiability of a quantified formula modulo a complete theory and an initial assignment. The optimized variant of $$\textsf{QSMA}$$ QSMA implemented in YicesQS is described and shown to preserve total correctness. A report on the performance of YicesQS at the 2022 SMT competition is included. YicesQS ran in the $$\textsf{LIA}$$ LIA , $$\textsf{NIA}$$ NIA , $$\textsf{LRA}$$ LRA , $$\textsf{NRA}$$ NRA , and $$\textsf{BV}$$ BV categories and ranked second for the “largest contribution” award (single queries). It was the only solver to solve all $$\textsf{LRA}$$ LRA instances, where it was about two orders of magnitude faster than the second best solver (Z3).