Template-Based Unbounded Time Verification of Affine Hybrid Automata

Computing over-approximations of all possible time trajectories is an important task in the analysis of hybrid systems. Sankaranarayanan et al. [20] suggested to approximate the set of reachable states using template polyhedra. In the present paper, we use a max-strategy improvement algorithm for computing an abstract semantics for affine hybrid automata that is based on template polyhedra and safely over-approximates the concrete semantics. Based on our formulation, we show that the corresponding abstract reachability problem is in co−NP. Moreover, we obtain a polynomial-time algorithm for the time elapse operation over template polyhedra.