Abstract
We examine a subclass of persistent Petri nets called single-path Petri nets. Our intention is to consider a class of Petri nets whose study might yield some insight into the mathematical properties of persistent Petri nets or even general Petri nets. We conjecture that the Karp-Miller coverability tree for a persistent net is small enough to be searched in polynomial space. Although we are unable to prove this conjecture, we do show that single-path Petri nets have this property. We then use this fact to show that the canonical analysis problems (i.e., boundedness, reachability, containment, and equivalence) for single-path Petri nets are PSPACE-complete in the strong sense. Furthermore, we show that the problem of recognizing a single-path Petri net is also PSPACE-complete.
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Howell, R.R., Jančar, P., Rosier, L.E. (1991). Single-path Petri nets. In: Tarlecki, A. (eds) Mathematical Foundations of Computer Science 1991. MFCS 1991. Lecture Notes in Computer Science, vol 520. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54345-7_63
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DOI: https://doi.org/10.1007/3-540-54345-7_63
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