Computing Uniform Interpolants for EUF via (conditional) DAG-based Compact Representations

The concept of a 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. This concept is precisely defined. Two algorithms for computing the uniform interpolant of a quantifier-free formula in 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 conjunction 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.