Approximated Reachability on Hybrid Automata: Falsification meets Certification

Undecidability of the reachability problem is ubiquitous in the context of hybrid automata. Being mostly based on either bounded reachability or on the notion of simulation preorder, current techniques for the approximated reachability analysis force to choose between under- and over-approximations.In this paper, we introduce a novel method for the reachability analysis of hybrid automata featuring (1) the ability of combining the certification and the falsification of reachability properties, and (2) the applicability to highly expressive families of hybrid automata, whose dynamics are not amenable to an exact representation.