Using linear algebra in decomposition of Farkas interpolants
Additional information
Authors
Blicha M.,
Hyvärinen A.,
Kofroň J.,
Sharygina N.
Type
Journal Article
Language
English
Abstract
The use of propositional logic and systems of linear inequalities over reals is a common means to model software for formal verification. Craig interpolants constitute a central building block in this setting for over-approximating reachable states, e.g. as candidates for inductive loop invariants. Interpolants for a linear system can be efficiently computed from a Simplex refutation by applying the Farkas’ lemma. However, these interpolants do not always suit the verification task - in the worst case, they can even prevent the verification algorithm from converging. 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 also present an efficient polynomial algorithm to compute decomposed interpolants and analyse its properties.We experimentally show that the use of decomposed interpolants inmodel checking results in immediate convergence on instances where state-of-the-art approaches diverge. Moreover, since being based on the efficient Simplex method, the approach is very competitive in general.
Keywords
Model checking, Satisfiability modulo theory, Linear real arithmetic, Craig interpolation
Journal
International journal on software tools for technology transfer
Volume
24
Pages (or article number)
111–125
Diffusion
License
CC BY
Visibility
Public
Status open access
Hybrid
