Anatomy of Alternating Quantifier Satisfiability (Work in progress)

11 pagesPublished: August 19, 2013

Abstract

We report on work in progress to generalize an algorithm recently introduced in [10] for checking
satisfiability of formulas with quantifier alternation. The algorithm uses two auxiliary procedures:
a procedure for producing a candidate formula for quantifier elimination and a procedure for eliminating
or partially eliminating quantifiers. We also apply the algorithm for Presburger Arithmetic
formulas and evaluate it on formulas from a model checker for Duration Calculus [8]. We report on
experiments on different variants of the auxiliary procedures. So far, there is an edge to applying
SMT-TEST proposed in [10], while we found that a simpler approach which just eliminates quantified
variables per round is almost as good. Both approaches offer drastic improvements to applying
default quantifier elimination.

Keyphrases: arithmetic, decision procedure, Presburger arithmetic, quantifier elimination, SMT

In: Pascal Fontaine and Amit Goel (editors). SMT 2012. 10th International Workshop on Satisfiability Modulo Theories, vol 20, pages 120--130