A Taxonomy of Fairness and Temporal Logic Problems for Petri Nets

In this paper, we define a temporal logic for reasoning about Petri nets. We show the model checking problem for this logic to be PTIME equivalent to the Petri net reachability problem. Using this logic and two refinements, we show the fair nontermination problem to be PTIME equivalent to reachability for several definitions of fairness. For other versions of fairness, this problem is shown to be either PTIME equivalent to the boundedness problem or highly undecidable. In all, 24 versions of fairness are examined.

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