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Zero-Safe Nets, or Transition Synchronization Made Simple.

Bruni, R.; Montanari, U.

In: Electronic Notes in Theoretical Computer Science, Vol. 7: Proceedings of EXPRESS'97, 4th workshop on Expressiveness in Concurrency, pages 1-19. Elsevier Science, 1997.

Abstract: In addition to ordinary places, called stable, zero-safe nets are equipped with zero places, which in a stable marking cannot contain any token. An evolution between two stable markings, instead, can be a complex computation called stable transaction, which may use zero places, but which is atomic when seen from stable places: no stable token generated in a transaction can be reused in the same transaction. Every zero-safe net has an ordinary Place-Transition net as its abstract counterpart, where only stable places are maintained, and where every transaction becomes a transition. The two nets allow us to look at the same system from both an abstract and a refined viewpoint. To achieve this result no new interaction mechanism is used, besides the ordinary token-pushing rules of nets. The refined zero-safe nets can be much smaller than their corresponding abstract P/T nets, since they take advantage of a transition synchronization mechanism. For instance, when transactions of unlimited length are possible in a zero-safe net, the abstract net becomes infinite, even if the refined net is finite. In the second part of the paper two universal constructions - both following the `Petri nets are monoids' approach and the collective token philosophy - are used to give evidence of the naturality of our definitions. More precisely, the operational semantics of zero-safe nets is characterized as an adjunction, and the derivation of abstract P/T nets as a coreflection.

Keywords: Petri nets are monoids, Abstraction, Transition synchronization, Transaction, Collective token philosophy.

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