an:06163649
Zbl 1410.68258
Praveen, M.
Small vertex cover makes Petri net coverability and boundedness easier
EN
Algorithmica 65, No. 4, 713-753 (2013).
00315648
2013
j
68Q85 05C70 68Q17 68Q25 68Q60
Petri nets; vertex cover; parameterized complexity; \textsc{ParaPspace}
Summary: The coverability and boundedness problems for Petri nets are known to be \textsc{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 \textsc{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 \textsc{ParaPspace} result to model checking a logic that can express some generalizations of coverability and boundedness.