Technical Report Number
Let Cn be the direct product of the bicyclic monoid C, taken n times, where n is a positive integer. It is shown that (1) every Petry net with n places can be represented by a finite subset of Cn represents a Petri net with n places, and (3) the firing rule of Petri net with n places, and (3) the firing rule of Petri nets can be defined as a faithful representation of Cn by the inverse hull of additive semigroup N^n is the set of natural numbers. A generalization of C, called 'link semigroup,' is defined, and the above results on Petri nets are derived as a special case of general property of the link semigroup.
Kimura, Takayuki D., "Algebraic Characterization of Petri Nets" Report Number: WUCS-79-8 (1979). All Computer Science and Engineering Research.