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An Event Structure Semantics for P/T Contextual Nets: Asymmetric Event Structures.

Baldan, P.; Corradini, A.; Montanari, U.

In: Nivat, M.: Lecture Notes in Computer Science, Vol. 1378: Proceedings of 5th Intern. Conf. on Foundations of Software Science and Computation Structures (FOSSaCS'98) held as part of the Europ. Conf. on Theory and Practice of Software, ETAPS'98 in Lisbon, Portugal, pages 63-80. Springer, April 1998.

Abstract: We propose an event based semantics for contextual nets, i.e. an extension of Place/Transition Petri nets where transitions can also have context conditions, modelling resources that can be read without being consumed. The result is a generalization of Winskel's work on safe nets: the event based semantics is given at categorical level via a chain of coreflections leading from the category WS-CN of weakly safe contextual nets to the category Dom of finitary prime algebraic domains. A fundamental rôle is played by the notion of asymmetric event strutures that generalize Winskel's prime event structures, follwing an idea similar to that of `possible flow' introduced by Pinna and Poigné. Asymmetric event structures have the usual causal relation of traditional prime event structures, but replace the symmetric conflict with a relation modelling asymmetric conflict of weak causality. Such relation allows oneto represent the new kind of dependency between events arising in contextual nets, as well as the usual symmetric conflict. Moreoverk it is used in a non-trivial way in the definition of the ordering of configurations, which is different from the standard set-inclusion.

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