Property-based Polynomial Invariant Generation using Sums-of-Squares Optimization
Résumé
While abstract interpretation is not theoretically restricted to specific kinds of properties, it is, in practice, mainly developed to compute linear over-approximations of reachable sets, aka. the collecting semantics of the program. The verification of user-provided properties is not easily compatible with the usual forward fixpoint computation using numerical abstract domains.
We propose here to rely on sums-of-squares programming to characterize a property-driven polynomial invariant. This invariant generation can be guided by either boundedness, or in contrary, a given zone of the state space to avoid.
While the target property is not necessarily inductive with respect to the program semantics, our method identifies a stronger inductive polynomial invariant using numerical optimization. Our method applies to a wide set of programs: a main while loop composed of a disjunction (if-
then-else) of polynomial updates e.g. piecewise polynomial controllers.
It has been evaluated on various programs.
Domaines
Informatique et langage [cs.CL]Origine | Fichiers produits par l'(les) auteur(s) |
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