Using linear algebra in decomposition of Farkas interpolants

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Using linear algebra in decomposition of Farkas interpolants

Popis výsledku v původním jazyce

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&apos; 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.

Název v anglickém jazyce

Using linear algebra in decomposition of Farkas interpolants

Popis výsledku anglicky

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&apos; 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA20-07487S" target="_blank" >GA20-07487S: Škálovatelné techniky pro analýzu komplexních vlastností počítačových systémů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International Journal on Software Tools for Technology Transfer

ISSN

1433-2779

e-ISSN

1433-2787

Svazek periodika

24

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

15

Strana od-do

111-125

Kód UT WoS článku

000681522900001

EID výsledku v databázi Scopus

2-s2.0-85111923705