On the decidability of the existence of polyhedral invariants in transition systems - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Acta Informatica Année : 2019

On the decidability of the existence of polyhedral invariants in transition systems

David Monniaux

Résumé

Automated program verification often proceeds by exhibiting inductive invariants entailing the desired properties. For numerical properties, a classical class of invariants is convex polyhedra: solution sets of system of linear (in)equalities. Forty years of research on convex polyhedral invariants have focused, on the one hand, on identifying “easier” subclasses, on the other hand on heuristics for finding general convex polyhedra. These heuristics are however not guaranteed to find polyhedral inductive invariants when they exist. To our best knowledge, the existence of polyhedral inductive invariants has never been proved to be undecidable. In this article, we show that the existence of convex polyhedral invariants is undecidable, even if there is only one control state in addition to the “bad” one. The question is still open if one is not allowed any nonlinear constraint.
Fichier principal
Vignette du fichier
article_Monniaux_computability_polyhedral_abstraction.pdf (113.79 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01587125 , version 1 (13-09-2017)
hal-01587125 , version 2 (09-05-2018)

Identifiants

Citer

David Monniaux. On the decidability of the existence of polyhedral invariants in transition systems. Acta Informatica, 2019, 56 (4), pp.385-389. ⟨10.1007/s00236-018-0324-y⟩. ⟨hal-01587125v2⟩
1104 Consultations
265 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More