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

Abstract : 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.
Type de document :
Pré-publication, Document de travail
Liste complète des métadonnées

Littérature citée [5 références]  Voir  Masquer  Télécharger

Contributeur : David Monniaux <>
Soumis le : mercredi 13 septembre 2017 - 16:42:41
Dernière modification le : mercredi 16 mai 2018 - 01:10:00
Document(s) archivé(s) le : jeudi 14 décembre 2017 - 15:19:48


Fichiers produits par l'(les) auteur(s)


  • HAL Id : hal-01587125, version 1
  • ARXIV : 1709.04382


David Monniaux. On the decidability of the existence of polyhedral invariants in transition systems. 2017. 〈hal-01587125v1〉



Consultations de la notice


Téléchargements de fichiers