Automated construction of compound Markov chains from generalized stochastic high-level Petri nets

A new type of Petri nets: Generalized Stochastic High-Level Petri nets (GSHLPN’s), collecting the qualities of GSPN’s and SHLPN’s, is presented. The automated construction of compound continuous-time Markov chains (CTMC’s) from GSHLPN’s is also considered. A formalism for the description of compound markings allowing a symbolic firing of the net to obtain a compound CTMC with correct state grouping is derived. The construction of the compound CTMC requires an algorithm to test the equivalence of compound markings. It is shown that, in the general case and for bounded number of rotation groups, the problem is polynomially equivalent to GRAPH ISOMORPHISM, a problem whose classification in the NP world is currently open