# Petri Net Part 15

## Tham khảo tài liệu 'petri net part 15', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Incremental Integer Linear Programming Models for Petri Nets Reachability Problems 411 Several approaches have been proposed to solve the Timed Petri net reachability problem either by restricting their study to a subclass of TPN like Timed Event Graphs where a place has exactly one input and one output transition either by using dedicated heuristics. A complete bibliography can be found in Richard 2000 . Since the fire of a Timed transition can occur as soon as it is fireable and as late as one wants there may exist from a given state an infinite number of reachable markings depending on the time and no reachability graph can be built. A first approach needs to consider Timed PN as a subclass of Time PN in order to use the state enumeration methods state class graphs proposed by Berthomieu and Diaz 1991 . On the other hand when dealing with early semantics a transition is fired as soon as it is fireable it is possible to proceed to an enumerative and structural analysis David and Alla 1992 . The early semantics has been extensively studied for the special class of Timed Event Graphs using max algebra Bacceli et al. 1992 . Since their structure does not handle conflicts it is possible to obtain linear equations corresponding to the complete behaviour of the net. In the following we will show that our incremental approach can lead to mathematical programming models in the most general case. 3. Incremental approaches As said before the state equation 3 does not bring enough information to solve the reachability problem in all cases. This comes from the fact that it does not take into account the fireability conditions 1 of the individual transitions fired in the sequence Ơ. Incremental approaches improve this formulation by considering a given number of step firings corresponding to parallel and reentrant transitions. In this section we discuss the interest of using steps and a fixed depth formulation. Step based reachability formulation Definition 14 Step . Let

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