From Strong Amalgamability to Modularity of Quantifier-Free Interpolation

• Published in: Automated Reasoning pp. 118 - 133
• Main Authors: Bruttomesso, Roberto, Ghilardi, Silvio, Ranise, Silvio
• Format: Book Chapter
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2012
• Series: Lecture Notes in Computer Science
• ISBN: 3642313647; 9783642313646
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-642-31365-3_12

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.