Abstract
In this paper we describe an abstract and (as we hope) a uniform frame for Petri net models, which enable to generalise algebra as well as enabling rule used in the dynamics of Petri nets. Our approach of such an abstract frame is based on using partial groupoids in Petri nets. Further, we study properties of Petri nets constructed in this manner through related labelled transition systems. In particular, we investigate the relationships between properties of partial groupoids used in Petri nets and properties of labelled transition systems crucial for the existence of the state equation and linear algebraic techniques. We show that partial groupoids embeddable to Abelian groups play an important role in preserving these properties.
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