Ground Interpolation for the Theory of Equality

Given a theory $\mathcal{T}$ and two formulas A and B jointly unsatisfiable in $\mathcal{T}$, a theory interpolant of A and B is a formula I such that (i) its non-theory symbols are shared by A and B , (ii) it is entailed by A in $\mathcal{T}$, and (iii) it is unsatisfiable with B in $\mathcal{T}$. Theory interpolants are used in model checking to accelerate the computation of reachability relations. We present a novel method for computing ground interpolants for ground formulas in the theory of equality. Our algorithm computes interpolants from colored congruence graphs representing derivations in the theory of equality. These graphs can be produced by conventional congruence closure algorithms in a straightforward manner. By working with graphs, rather than at the level of individual proof steps, we are able to derive interpolants that are pleasingly simple (conjunctions of Horn clauses) and smaller than those generated by other tools.