Summary
Three notions of distance for measuring the synchronic dependence of transition firings in Petri nets are studied. For the first two notions we present algorithms for obtaining a basis of the linear space of weight vectors for which the distance is finite, and methods for computing the distance for any given weight vector by examining a finite set of vectors obtained a priori. For the third notion of distance, the problem of deciding whether a given weight vector yields a finite distance is shown to be equivalent to the reachability problem. Finally it is shown that a basis of the linear space of weight vectors for which the weighted sum of token counts is bounded over all reachable markings can be obtained effectively. Also some complexity results are given.
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Suzuki, I., Kasami, T. Three measures for synchronic dependence in Petri nets. Acta Informatica 19, 325–338 (1983). https://doi.org/10.1007/BF00290730
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DOI: https://doi.org/10.1007/BF00290730