Merge and Conquer: State Merging in Parametric Timed Automata

Parameter synthesis for real-time systems aims at synthesizing dense sets of valuations for the timing requirements, guaranteeing a good behavior. A popular formalism for modeling parameterized realtime systems is parametric timed automata (PTAs). Compacting the state space of PTAs as much as possible is fundamental. We present here a state merging reduction based on convex union, that reduces the state space, but yields an over-approximation of the executable paths. However, we show that it preserves the sets of reachable locations and executable actions. We also show that our merging technique associated with the inverse method, an algorithm for parameter synthesis, preserves locations as well, and outputs larger sets of parameter valuations.