The use of interpolants in verification is gaining more and more importance. Since theories used in applications are usually obtained as (disjoint) combinations of simpler theories, it is important to modularly re-use interpolation algorithms for the component theories. We show that a sufficient and necessary condition to do this for quantifier-free interpolation is that the component theories have the 'strong (sub-)amalgamation' property. Then, we provide an equivalent syntactic characterization, identify a sufficient condition, and design a combined quantifier-free interpolation algorithm handling both convex and non-convex theories, that subsumes and extends most existing work on combined interpolation. © 2012 Springer-Verlag.
From strong amalgamability to modularity of quantifier-free interpolation / Bruttomesso, R.; Ghilardi, S.; Ranise, S.. - 7364:(2012), pp. 118-133. (Intervento presentato al convegno 6th International Joint Conference on Automated Reasoning, IJCAR 2012 tenutosi a Manchester, gbr nel 2012) [10.1007/978-3-642-31365-3_12].
From strong amalgamability to modularity of quantifier-free interpolation
Ranise S.
2012-01-01
Abstract
The use of interpolants in verification is gaining more and more importance. Since theories used in applications are usually obtained as (disjoint) combinations of simpler theories, it is important to modularly re-use interpolation algorithms for the component theories. We show that a sufficient and necessary condition to do this for quantifier-free interpolation is that the component theories have the 'strong (sub-)amalgamation' property. Then, we provide an equivalent syntactic characterization, identify a sufficient condition, and design a combined quantifier-free interpolation algorithm handling both convex and non-convex theories, that subsumes and extends most existing work on combined interpolation. © 2012 Springer-Verlag.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
