Work

On the Monniaux Problem in Abstract Interpretation

Year: 2024

Type: article

Abstract: The Monniaux Problem in abstract interpretation asks, roughly speaking, whether the following question is decidable: Given a program P , a safety (e.g., non-reachability) specification \(\varphi\) , and an abstract domain of invariants \(\mathcal {D}\) , does there exist an inductive invariant \(\mathcal {I}\) in \(\mathcal {D}\) guaranteeing that program P meets its specification φ? The Monniaux Problem is of course parameterised by the classes of programs and invariant domains that one considers. In this article, 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.

Source: Journal of the ACM

DOI: 10.1145/3704632

Authors: Nathanael Fijalkow, Engel Lefaucheux, Pierre Ohlmann, Joël Ouaknine, Amaury Pouly, James Worrell

Institutions: Centre National de la Recherche Scientifique, Université de Bordeaux, Laboratoire Bordelais de Recherche en Informatique, Max Planck Institute for Software Systems, Institut de Recherche en Informatique Fondamentale, University of Oxford

Language: English

Topic: Logic, programming, and type systems

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze

Funders: Deutsche Forschungsgemeinschaft, Engineering and Physical Sciences Research Council

OpenAlex ID: W4404474826

FWCI:

Cites: 31

Cited by:

Related to: 10