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Small vertex cover makes Petri net coverability and boundedness easier. (English) Zbl 1410.68258
Summary: The coverability and boundedness problems for Petri nets are known to be Expspace-complete. Given a Petri net, we associate a graph with it. With the vertex cover number \(k\) of this graph and the maximum arc weight \(W\) as parameters, we show that coverability and boundedness are in ParaPspace. This means that these problems can be solved in space \(\mathcal{O} ({\operatorname{ef}}(k, W){\operatorname{poly}}(n))\), where \(\operatorname{ef}(k,W)\) is some super-polynomial function and \(\operatorname{poly}(n)\) is some polynomial in the size of the input \(n\). We then extend the ParaPspace result to model checking a logic that can express some generalizations of coverability and boundedness.
MSC:
68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
68Q25 Analysis of algorithms and problem complexity
68Q60 Specification and verification (program logics, model checking, etc.)
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