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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Ground Interpolation for the Theory of Equality
verfasst von : Alexander Fuchs, Amit Goel, Jim Grundy, Sava Krstić, Cesare Tinelli
Erschienen in: Tools and Algorithms for the Construction and Analysis of Systems
Verlag: Springer Berlin Heidelberg
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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.