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Simulation of Timed Petri Nets by Ordinary Petri Nets and Applications to Decidability of the Timed Reachability Problem.

Valero Ruíz, V.; de Frutos Escrig, D.; Cuartero Gómez, F.

In: Proc. 4th Int. Workshop on Petri Nets and Performance Models (PNPM'91), Melbourne, Australia, pages 154-163. IEEE Comp. Soc. Press, December 1991.

Abstract: In this paper we consider Timed Petri Nets, for which a timed step semantics generalizing the ordinary step semantics is presented. A codification of them, with regard to such semantics, by Ordinary Petri Nets is presented. This codification is presented in a gradual way, beginning with that corresponding to a more resticted and thus simpler step semantics. This semantics does not allow the overlapped firing of several instances of each transition. Next, we consider a step semantics which allows such overlapped executions, but not the simultaneous firing of several instances of the same transition. In both restricted cases the construction is based on an automaton which controls the system evolution. The construction for the most general semantics is rather more complicated, that is why it is presented gradually. We consider three versions of it, being the two first ones easier to understand, but having each one a different problem that we would probably like to avoid; this is made by the third construction, which refines the previous ones. Finally, we use this simulation to decide several problems on Timed Petri Nets.

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