Property-based Polynomial Invariant Generation using Sums-of-Squares Optimization

Assalé Adjé (1) , Pierre-Loïc Garoche (1) , Victor Magron (2)

1 ONERA - The French Aerospace Lab [Toulouse]
2 Imperial College London

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]

Assalé Adjé, Pierre-Loïc Garoche, Victor Magron. Property-based Polynomial Invariant Generation using Sums-of-Squares Optimization. 2015. ⟨hal-01134816⟩