Fast Approximations of Quantifier Elimination

Isabel Garcia-Contreras*, V. K.Hari Govind, Sharon Shoham, Arie Gurfinkel

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


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

Original languageEnglish
Title of host publicationComputer Aided Verification - 35th International Conference, CAV 2023, Proceedings
EditorsConstantin Enea, Akash Lal
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages23
ISBN (Print)9783031377020
StatePublished - 2023
EventProceedings of the 35th International Conference on Computer Aided Verification, CAV 2023 - Paris, France
Duration: 17 Jul 202322 Jul 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13965 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceProceedings of the 35th International Conference on Computer Aided Verification, CAV 2023


FundersFunder number
MathWorks Inc.
Microsoft Research
Horizon 2020 Framework Programme759102-SVIS
Natural Sciences and Engineering Research Council of Canada
European Research Council
Israel Science Foundation1810/18


    Dive into the research topics of 'Fast Approximations of Quantifier Elimination'. Together they form a unique fingerprint.

    Cite this