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In learning about Timed Automata, Coloured Petri Nets, and Process Calculi, I am wondering what the benefit is of having the Petri Net transition be a separate type of node in Petri Nets.

It seems that you can model the same stuff (eventually) using Timed Automata or Process Calculi, which both only have states and transitions (as edges, not objects). Instead of transition nodes, you could just have two types of "state", one be the Petri net place, the other be the Petri net transition. Then this second node does all it's queuing/guarding/checking of the tokens and whatnot. So I'm not sure the benefit is of having transition be a separate object in Petri Nets, when it could just be a second kind of "place" or "state".

That makes me wonder if there is a generalization of Petri nets to arbitrary number of node types (where instead of just place/transition, you have x, y, z, ...). In this sense it seems that process calculi are a generalization of Petri Nets.

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The state transition graph underlying a Petri Net model is called the Reachability Graph. Yes, it exists, and it is the foundation of Petri Net semantics. However, it is possible to define simple, easily understandable Petri Net models that have reachability graphs of a size and structure that no human could make sense of. They might also be graphs with an infinite number of states.

It's similar to programming languages: every conceivable algorithm or program could be written in assembly language. But there are dozens, if not hundreds, of higher level programming languages that make it easier, simpler, and faster for humans to write and understand programs, to express the algorithms and the processing they need to implement. And then a compiler or interpreter turns the high-level program into a stream of processor instructions.

Petri Nets are meant as a way for humans to create meaningful, understandable models, without drilling down to individual states and transitions. Then Petri Net tools handle the simulation and/or analysis of the models.

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