Petri Net Part 9

Tham khảo tài liệu 'petri net part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | From Time Petri Nets to Timed Automata 231 reachable in T if there is a state M v 6 ReachState T . The set of reachable markings of T is denoted ReachMark T . If the set ReachMark T is finite we say that T is bounded otherwise it is unbounded. If we add two sets of markings F final and R repeated we can define the languages accepted by T. We let Sf resp. Sr be the set of states M v of St . M 6 F resp. M 6 R . The timed language L T accepted by T is the timed language accepted by St with sets Sf and Sr as final and repeated states. Similar definitions hold for L T and Lw T . Moreover for a labeled TPN T L the languages accepted by T L are the languages accepted by T where in each timed word a transition label t is replaced by L t . In Definition 7 we have implicitly assumed that the constraints given on each transition of the TPN by the mapping a ft are closed constraints. We can also consider that the firing intervals of a transition are left and or right open. The semantics is defined accordingly substituting to assume a ti f ti is left-closed and right open in this case the discrete transition relation for ti is defined using a ti Vi f ti instead of a ti Vi f ti in Definition 7 and for the continuous transition relation we should use Vị f ti . Most of the results we give in this chapter hold for any type of intervals. In the sequel we denote TPN the most general class of TPNs using open or closed intervals and TPN for the subclass that uses only closed intervals. Our semantics Bérard et al. 2005a Cassez and Roux 2006 is based on the common definition of Berthomieu and Diaz 1991 Aura and Lilius 2000 for safe TPNs but still there are some advantages using ours. First previous formal semantics Berthomieu and Diaz 1991 Lilius 1998 Pezzè 1999 Aura and Lilius 2000 for TPNs required the TPNs to be safe. Our semantics encompasses the whole class of TPNs and is fully consistent with the previous semantics when restricted to safe TPNs5. Thus we have given a semantics to

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