Deriving Parameter Conditions For Periodic Timed Automata Satisfying Real-Time Temporal Logic Formulas

A symbolic model checking method for parametric periodic timed automata is proposed. The method derives symbolically the weakest condition for parameters such that the specified control state of a periodic timed automaton satisfies some temporal properties. Unlike several existing parametric symbolic model checking methods, the proposed method is `on-the-fly' --- it does not unnecessarily check all the states. Instead, it traverses some necessary part of the computation tree to derive the weakest condition. We show that if we constrain a timed automaton to be periodic, i.e. if we force a timed automaton to return to its initial state periodically at the specified constant time, we have only to traverse at most the first 3 periods in the infinite computation tree. In the proposed method, we can avoid a costly (and generally undecidable) fixpointcalculation for dense-time-domain state sets, and derive the weakest condition for parameters of a timed automaton to satisfy given temporal properties written in a real-time temporal logic formula. Keywords: symbolic model checking, real-time periodic system, temporal logic 1