Representing Place / Transition Nets in Span(Graph)

摘要

The compact closed bicategory Span of spans of reflexive graphs is described and it is interpreted as an algebra for constructing specifications of concurrent systems. We describe a procedure for associating to any Place/Transition system #OMEGA# an expression #psi#_#OMEGA# in the algebra Span. The value of this expression is a system whose behaviours are the same as those of the P/T system. Furthermore, along the lines of Penrose's string diagrams, a geometry is associated to the expression #psi#_#OMEGA which is essentially the same geometry as that usually associated to the net underlying #OMEGA#.