Ground Interpolation for the Theory of Equality

  • Authors:

  • Alexander Fuchs;Amit Goel;Jim Grundy;Sava Krstić;Cesare Tinelli

  • Affiliations:

  • Department of Computer Science, The University of Iowa,;Strategic CAD Labs, Intel Corporation,;Strategic CAD Labs, Intel Corporation,;Strategic CAD Labs, Intel Corporation,;Department of Computer Science, The University of Iowa,

  • Venue:
  • TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
  • Year:
  • 2009

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Abstract

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.