The semantics of capacities in P/T nets
Advances in Petri nets 1989
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Petri Nets over Partial Algebra
Unifying Petri Nets, Advances in Petri Nets
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Process semantics of Petri nets over partial algebra
ICATPN'00 Proceedings of the 21st international conference on Application and theory of petri nets
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In the paper we study "first consume then produce" and "first produce then consume" causality of transition firings in Petri nets over partial algebra. We show that both causalities may be described by simple algebraic operations on transition systems, namely the compatible and linear operation. Thus, weak semantics (weak marking graph) corresponding to the "first consume then produce" causality is constructed by compatible operation on related net. Strong semantics (strong marking graph), which corresponds to consumption and production in any order, i.e., to combination of both causalities, is given by intersection of compatible and linear image of the related net. Furthermore, it is shown that the classes of weak and strong marking graphs of all Petri nets over arbitrary partial groupoids are equivalent up to isolated markings. The same equivalence is shown for classes of weak and strong marking graphs of all Petri nets over partial groupoids embeddable into Abelian groups.