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arXiv · 2002.09784

Uniform Interpolants in EUF: Algorithms using DAG-representations

Silvio Ghilardi·Alessandro Gianola·Deepak Kapur
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Abstract

The concept of uniform interpolant for a quantifier-free formula from a given formula with a list of symbols, while well-known in the logic literature, has been unknown to the formal methods and automated reasoning community for a long time. This concept is precisely defined. Two algorithms for computing quantifier-free uniform interpolants in the theory of equality over uninterpreted symbols (EUF) endowed with a list of symbols to be eliminated are proposed. The first algorithm is non-deterministic and generates a uniform interpolant expressed as a disjunction of conjunctions of literals, whereas the second algorithm gives a compact representation of a uniform interpolant as a conjunction of Horn clauses. Both algorithms exploit efficient dedicated DAG representations of terms. Correctness and completeness proofs are supplied, using arguments combining rewrite techniques with model theory.

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Silvio Ghilardi, Alessandro Gianola, Deepak Kapur. 2020-02-22. Uniform Interpolants in EUF: Algorithms using DAG-representations. https://doi.org/10.46298/lmcs-18(2%3A2)2022

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