On the Upward/Downward Closures of Petri Nets
نویسندگان
چکیده
We study the size and the complexity of computingfinite state automata (FSA) representing and approximatingthe downward and the upward closure of Petri net languageswith coverability as the acceptance condition. We show how toconstruct an FSA recognizing the upward closure of a Petri netlanguage in doubly-exponential time, and therefore the size is atmost doubly exponential. For downward closures, we prove thatthe size of the minimal automata can be non-primitive recursive.In the case of BPP nets, a well-known subclass of Petri nets, weshow that an FSA accepting the downward/upward closure canbe constructed in exponential time. Furthermore, we considerthe problem of checking whether a simple regular language isincluded in the downward/upward closure of a Petri net/BPP netlanguage. We show that this problem is EXPSPACE-complete(resp. NP-complete) in the case of Petri nets (resp. BPP nets).Finally, we show that it is decidable whether a Petri net languageis upward/downward closed.
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