Generalized Stochastic Petri Nets vs. Stochastic Timed Automata

 

 

We want to compare two formalisms based on their modeling power.  We understand the modeling power in the following way - two formalisms have equivalent modeling power if they can model the same class of (discrete-event) systems.

 

Consider the following connections between Petri Nets and State Automata. It is easy to show that given any finite state automaton it can be directly turned into a Petri Net by simple replacing the events of the automaton with the transitions of the Petri Net with one input and one output. On the other hand for any Petri Net we can construct a reachability graph and the resulting graph will itself be a state automaton, since we allow the state set of an automaton to be countably infinite. ( ? It is still unclear though how to go from an arbitrary state automaton with infinite number of states to a Petri Net…?).

 

Another complication arises from the fact that these mappings only deal with untimed deterministic models. For formalisms in consideration we also need to consider how to map stochastic clock structures and probabilistic transitions from Petri Nets to State Automata and back. (? This may be not trivial…?)

 

 

 

References:

1.      C. G. Cassandras, S. Lafortune,  Introduction to Discrete Event Systems, Kluwer, 1999.