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Completeness Results for Generalized Communication-free Petri Nets with Arbitrary Arc Multiplicities

Mayr E. W., Weihmann J.

Fundamenta Informaticae

2016

Vol. 143, nr 3/4

355--391

We investigate gcf-Petri nets, a generalization of communication-free Petri nets allowing arbitrary arc multiplicities, and characterized by the sole restriction that each transition has at most one incoming arc. We use canonical firing sequences with nice properties for gcf-PNs to show that the RecLFS, (zero-)reachability, covering, and boundedness problems of gcf-PNs are in PSPACE. By simulating PSPACE-Turing machines by gss-PNs, a subclass of gcf-PNs where additionally all transitions have at most one outgoing arc, we ultimately obtain PSPACE-completess for these problems in case of gss-PNs or gcf-PNs. Additionally, we prove PSPACE-completeness for the liveness problem of gcf-PNs. Last, we show PSPACE-hardness as well as a doubly exponential space upper bound for the containment and equivalence problems of gss-PNs or gcf-PNs.

Complexity Results for Problems of Communication-Free Petri Nets and Related Formalisms

Mayr E. W., Weihmann J.

Fundamenta Informaticae

2015

Vol. 137, nr 1

61--86

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.