Abstract
We investigate several computational problems of communication-free Petri nets, and develop very efficient mostly linear time algorithms for different variations of the boundedness and liveness problems of cf-PNs. For several more complex notions of boundedness, as well as for the covering problem, we show NP-completeness. In the last part, we use our results for cf-PNs to give linear time algorithms for related problems of context-free commutative grammars, and, in turn, use known results for such grammars to give a coNEXPTIME-upper bound for the equivalence problem of cf-PNs.
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