PTIME Parametric Verification of Safety Properties for Reasonable Linear Hybrid Automata

This paper identifies an industrially relevant class of linear hybrid automata (LHA) called reasonable LHA for which parametric verification of convex safety properties with exhaustive entry states can be verified in polynomial time and time-bounded reachability can be decided in nondeterministic polynomial time for non-parametric verification and in exponential time for parametric verification. Properties with exhaustive entry states are restricted to runs originating in a (specified) inner envelope of some mode-invariant. Deciding whether an LHA is reasonable is shown to be decidable in polynomial time.