A Memo on Computability in Time Petri Nets

Time Petri nets were introduced by Merlin in [5] in order to study recoverability problems in computer systems and the design of communication protocols. Berthomieu and Menasche in [2] res. Berthomieu and Diaz in [1] provide a method for the analysis of the qualitative behavior of the net. They divide the state spaces in state classes which are describe by a marking and time domain given by inequalities. The reachability graph is defined as a directed graph where the vertices are the reachable state classes and the edges are labeled by transitions. The net time is taken into account in the reachability graph by means of the inequalities which describe the state classes. This is a disadvantage for a quantitative analysis of the TPN. The reachability graph has the property, that the graph is finite iff the TPN is bounded. A similar definition for a reachability graph for a TPN delivers [3]. The property from above namely that the graph is finite iff the TPN is bounded is also true for the reachability graph defined here. In contrast to above, the time appears explicitly in this reachability graph as weights on some edges of the graph. Moreover, the vertices contain no information. Thus, our reachability graph is a usual directed weighted graph. Therefore, it is now possible to use the graph theory in order to accomplish quantitative analysis.