# UNIFORM INTERPOLANTS IN *UF*: ALGORITHMS USING DAG-REPRESENTATIONS

LOGICAL METHODS IN COMPUTER SCIENCE（2022）

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 (epsilon UF) 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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Key words

Uniform Interpolation,epsilon UF,DAG representation,term rewriting

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