A geometric approach to bisimulation and verification of hybrid systems

The paper opens up avenues for applying model checking algorithms to the verification of safety problems for hybrid systems consisting of coordinating autonomous agents, and especially hybrid systems where the continuous level is a model of the kinematic dynamics. There are some limitations and obstacles to be overcome. First, it is likely that model checking will still be a computationally expensive tool. Initially, the number of autonomous agents will be small and the continuous dynamics will be low-dimensional, at least until further breakthroughs appear on this frontier. The approach becomes more interesting when more of the burden of control can be placed at the logic level, for the performance of model checking is relatively unaffected by the number of states of the automaton. Some work that remains to be done is obtaining the approximate automaton automatically, given the analytical representation of its bisimulation, and to characterize the robustness of the reach set to model variations.