Fast Approximations of Quantifier Elimination

Abstract Quantifier elimination (qelim) is used in many automated reasoning tasks including program synthesis, exist-forall solving, quantified SMT, Model Checking, and solving Constrained Horn Clauses (CHCs). Exact qelim computationally expensive. Hence, it often approximated. For example, Z3 uses “light” pre-processing to reduce the number of variables. CHC-solver Spacer model-based projection (MBP) under-approximate relative a given model, over-approximations can be as abstractions. In this paper, we present QEL framework for fast approximations qelim. provides uniform interface both quantifier reduction projection. builds on egraph data structure – core EUF decision procedure SMT by casting problem choosing ground (i.e., variable-free) representatives equivalence classes. We have implement MBP theories Arrays Algebraic Data Types (ADTs). integrated our new evaluated within several that rely approximations, outperforming state-of-the-art.