On the Monniaux Problem in Abstract Interpretation - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2019

On the Monniaux Problem in Abstract Interpretation

Résumé

The Monniaux Problem in abstract interpretation asks, roughly speaking, whether the following question is decidable: given a program $P$, a safety (\emph{e.g.}, non-reachability) specification $\varphi$, and an abstract domain of invariants $\mathcal{D}$, does there exist an inductive invariant $I$ in $\mathcal{D}$ guaranteeing that program $P$ meets its specification $\varphi$. The Monniaux Problem is of course parameterised by the classes of programs and invariant domains that one considers. In this paper, we show that the Monniaux Problem is undecidable for unguarded affine programs and semilinear invariants (unions of polyhedra). Moreover, we show that decidability is recovered in the important special case of simple linear loops.

Dates et versions

hal-02395773 , version 1 (05-12-2019)

Identifiants

Citer

Nathanaël Fijalkow, Engel Lefaucheux, Pierre Ohlmann, Joël Ouaknine, Amaury Pouly, et al.. On the Monniaux Problem in Abstract Interpretation. SAS, 2019, Porto, Portugal. ⟨hal-02395773⟩
42 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More