An algebra for constructing Petri nets as transition systems

Giulio Katis – 23 April 1997

The discrete Cartesian bicategory Span(ReflexiveGraphs) is described and it is interpreted as an algebra of transition systems. We describe a procedure for associating to any Petri net N an expression E(N) in the algebra Span(ReflexiveGraphs). The valuation of this expression is a transition system whose behaviors are the same as those of the net. Furthermore, via a mild generalization of Penrose's string diagrams, a geometry is associated to E(N), this being essentially the same geometry as that usually associated to the net N.