## Book chapter

Title:

Decomposing Farkas Interpolants

Publication:

Tools and Algorithms for the Construction and Analysis of Systems

Year:

2019

ISBN:

978-3-030-17461-3 978-3-030-17462-0

Abstract:

Modern veriﬁcation commonly models software with Boolean logic and a system of linear inequalities over reals and overapproximates the reachable states of the model with Craig interpolation to obtain, for example, candidates for inductive invariants. Interpolants for the linear system can be eﬃciently constructed from a Simplex refutation by applying the Farkas’ lemma. However, Farkas interpolants do not always suit the veriﬁcation task and in the worst case they may even be the cause of divergence of the veriﬁcation algorithm. This work introduces the decomposed interpolants, a fundamental extension of the Farkas interpolants obtained by identifying and separating independent components from the interpolant structure using methods from linear algebra. We integrate our approach to the model checker Sally and show experimentally that a portfolio of decomposed interpolants results in immediate convergence on instances where state-of-the-art approaches diverge. Being based on the eﬃcient Simplex method, the approach is very competitive also outside these diverging cases.

BibTeX:

@incollection{vojnar_decomposing_2019, title = {{Decomposing Farkas Interpolants}}, author = {Blicha, Martin and Hyvärinen, Antti E. J. and Kofroň, Jan and Sharygina, Natasha}, year = {2019}, booktitle = {{Tools and Algorithms for the Construction and Analysis of Systems}}, editor = {Vojnar, Tomáš and Zhang, Lijun}, publisher = {Springer International Publishing}, location = {Cham}, doi = {10.1007/978-3-030-17462-0_1}, isbn = {978-3-030-17461-3 978-3-030-17462-0}, pages = {3--20}, url = {http://link.springer.com/10.1007/978-3-030-17462-0_1}, volume = {11427}, }