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.

@article{paperbot1709,
  title = {Uniform Interpolants in EUF: Algorithms using DAG-representations},
  author = {Silvio Ghilardi and Alessandro Gianola and Deepak Kapur},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 18, Issue 2},
  year = {2022},
  doi = {10.46298/lmcs-18(2:2)2022}
}