# Cesare Tinelli's Publications

Alexander Fuchs,
Amit Goel,
Jim Grundy,
Sava Krstić,
and Cesare Tinelli.

**Ground Interpolation for the Theory of Equality**. In*Proceedings of the 15th Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS'09)*, York, UK, 2009.Abstract.Given a theoryTand two formulasAandBjointly unsatisfiable inT, a theory interpolant ofAandBis a formulaIsuch that(i)its non-theory symbols are shared byAandB,(ii)it is entailed byAinT, and(iii)it is unsatisfiable withBinT. 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.