Using linear algebra in decomposition of Farkas interpolants

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10430252" target="_blank" >RIV/00216208:11320/22:10430252 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Saupygyd2R" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Saupygyd2R</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10009-021-00641-z" target="_blank" >10.1007/s10009-021-00641-z</a>

Result language
angličtina
Original language name
Using linear algebra in decomposition of Farkas interpolants
Original language description
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 in model 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.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/GA20-07487S" target="_blank" >GA20-07487S: Scalable Techniques for Analysis of Complex Properties of Computer Systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical
International Journal on Software Tools for Technology Transfer
ISSN
1433-2779
e-ISSN
1433-2787
Volume of the periodical
24
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
15
Pages from-to
111-125
UT code for WoS article
000681522900001
EID of the result in the Scopus database
2-s2.0-85111923705

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