Wednesday, February 01, 2012

Petri nets and Span(Graph) II

I mentioned in the last post the close relation between Petri nets and multigraphs. (I  will ignore the difference between them in these remarks.) Of course I was speaking only of the net structure, not the states and dynamics (though a suggested categorical dynamics of a Petri net/multigraph may be obtained by considering the free symetric monoidal category on the multigraph - Meseguer, Montanari).

 I want to make one comparison between Petri nets and Span(Graph) (introduced at AMAST in 1997). As I have said in the penultimate post, expressions in Span(Graph) yield (cospans of) multigraphs, and hence Petri nets. However the vertices and arcs of the multigraph coming from an expression in Span(Graph) are labelled with automata. Instead, for a Petri net the vertices (places) have only an associated state, and the arcs (transitions) have a simple uniform firing rule.

One possible view of an expression in Span(Graph) is that it is a Petri net with programmable dynamics.

A big advantage of Span(Graph) is that it is a compositional theory.



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