TY - GEN
T1 - Fast Approximations of Quantifier Elimination
AU - Garcia-Contreras, Isabel
AU - Govind, V. K.Hari
AU - Shoham, Sharon
AU - Gurfinkel, Arie
N1 - Publisher Copyright:
© 2023, The Author(s).
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85172235058&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-37703-7_4
DO - 10.1007/978-3-031-37703-7_4
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AN - SCOPUS:85172235058
SN - 9783031377020
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 64
EP - 86
BT - Computer Aided Verification - 35th International Conference, CAV 2023, Proceedings
A2 - Enea, Constantin
A2 - Lal, Akash
PB - Springer Science and Business Media Deutschland GmbH
T2 - Proceedings of the 35th International Conference on Computer Aided Verification, CAV 2023
Y2 - 17 July 2023 through 22 July 2023
ER -