Synthesizing Parametric Constraints on Various Case Studies Using IMITATOR (Preliminary Version)

We consider in this report systems modeled by timed automata. The timing bounds involved in the action guards and location invariants of our timed automata are not constants, but parameters. Those parametric timed automata allow to model various kinds of timed systems, e.g. communication protocols or asynchronous circuits. We will also assume that we are given an initial tuple π0 of values for the parameters, which corresponds to values for which the system is known to behave properly. Our goal is to compute a constraint K0 on the parameters, satisfied by π0, guaranteeing that, under any parameter valuation satisfying K0, the system behaves in the same manner : for any two parameter valuations satisfying K0, the behaviors of the timed automata are (time-abstract) equivalent, i.e., the traces of execution viewed as alternating sequences of actions and locations are identical. We present in this report several applications of the program IMITATOR implementing the algorithm InverseMethod, as described in [2]. We shortly recall the algorithm InverseMethod and its implementation IMITATOR in Sect. 2. We then present various case studies from the literature : two memory circuits, i.e., a flip-flop circuit (Sect. 3), and “and–or” circuit (Sect. 4), and three protocols, i.e., the root contention protocol (Sect. 5), the bounded retransmission protocol (Sect. 7) and the CSMA/CD protocol (Sect. 6). We then present two real case studies : a portion of the memory circuit SPSMALL designed by ST-Microelectronics (Sect. 8), and a distributed control system (Sect. 9). We finally summarize the experiments in Sect. 10. All experiments were conduced on an Intel Quad Core 3 GHz with 3.2 Gb.