Using linear algebra in decomposition of Farkas interpolants

Abstract The use of propositional logic and systems linear inequalities over reals is a common means to model software for formal verification. Craig interpolants constitute central building block in this setting over-approximating reachable states, e.g. as candidates inductive loop invariants. Interpolants system can be efficiently computed from Simplex refutation by applying the Farkas’ lemma. However, these do not always suit verification task—in worst case, they even prevent algorithm converging. This work introduces decomposed interpolants, fundamental extension Farkas obtained identifying separating independent components interpolant structure, using methods algebra. We also present an efficient polynomial compute analyse its properties. experimentally show that checking results immediate convergence on instances where state-of-the-art approaches diverge. Moreover, since being based method, approach very competitive general.