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Journal article

Using linear algebra in decomposition of Farkas interpolants

  • Blicha, Martin Facoltà di scienze informatiche, Università della Svizzera italiana, Svizzera - Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic
  • Hyvärinen, Antti E. J. Facoltà di scienze informatiche, Università della Svizzera italiana, Svizzera
  • Kofroň, Jan Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic
  • Sharygina, Natasha Facoltà di scienze informatiche, Università della Svizzera italiana, Svizzera
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    05.08.2021
Published in:
  • International journal on software tools for technology transfer. - Springer. - 2021, p. 15
Model checking
Satisfiability modulo theory
Linear real arithmetic
Craig interpolation
English 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.
Language
  • English
Classification
Computer science and technology
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https://n2t.net/ark:/12658/srd1319222
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