Falsification of LTL safety properties in hybrid systems

This paper develops a novel approach for the falsification of safety properties given by a syntactically safe linear temporal logic (LTL) formula $${\phi}$$ for hybrid systems with nonlinear dynamics and input controls. When the hybrid system is unsafe, the approach computes a trajectory that indicates violation of $${\phi}$$ . The approach is based on an effective combination of model checking and motion planning. Model checking searches on-the-fly the automaton of $${\neg\phi}$$ and an abstraction of the hybrid system for a sequence σ of propositional assignments that violates $${\phi}$$ . Motion planning incrementally extends trajectories that satisfy more and more of the propositional assignments in σ. Model checking and motion planning regularly exchange information to find increasingly useful sequences σ for extending the current trajectories. Experiments that test LTL safety properties on a robot navigation benchmark modeled as a hybrid system with nonlinear dynamics and input controls demonstrate the computational efficiency of the approach. Experiments also indicate significant speedup when using minimized DFA instead of non-minimized NFA for representing $${\neg\phi}$$ .