It may sound difficult to deal with an arbitrary Petri Net and therefore conflict-free decomposition for some special kinds of Petri Net may be also helpful for my case. Because the conflict-free Petri Net is easy to be analyzed, divide-and-conquer notion can be realized for large-scale system analysis.
Not exactly an answer to your question but related.
In my previous work, I discuss how arbitrary Petri net executions can be decomposed into segments that are defined over marked graph (i.e conflict-free Petri Net) essentially following the same reasoning you have about theirs analysis .
Conference Paper Verifying Modal Workflow Specifications Using Constraint Solving
I know that a safe persistent net can be transformed into a marked graph by duplicating some transitions and places. You can look at the work by Ramamoorthy and Ho. "Performance evaluation of asynchronous concurrent system using Petri nets".
I dealt with superficially with the matter. You can get some references form internet by means of the following keywords:
Superposed Automata Nets
the related theme were deeply developed by Fiorella De Cindio, Giorgio de Michelis and Lucia Pomello from Milan UNiversity years ago.
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