2015/03/24 by Adjé, Assalé, Garoche, Pierre-Loïc, Magron, Victor · 2 citations
#FOS: Computer and information sciences #Logic in Computer Science (cs.LO)
paper · doi:10.48550/arxiv.1503.07025
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.