A Synthesis Method for Petri Net with Prescribed Firing Sequence
指定点弧系列をもつペトリネットの合成方法

Kouji TAKAHASHI, Kensuke HASEGAWA, Zbigniew BANASZAK
1985 Transactions of the Society of Instrument and Control Engineers  
The paper describes an algorithm to synthesize a Petri net which can generate a given firing sequence. The Petri net is one of the effective tools to represent event-condition systems which act asynchronously and concurrently, such as production systems in which work pieces, data or informations are processed in order by the system components. As we realize such systems including system control, how to realize the processing order given and how to arbitrate conflicts are fundamental problems.
more » ... king them into consideration, the authors propose the synthesis algorithm of a Petri net which is able to generate a given firing sequence. In a Petri net, the activation of a system component may correspond to either a firing of a transition or a token in a place. In the paper, however, the authors decided that the activation corresponds to a firing of a transition, then the firing sequence of the transitions is regarded as the order of the process. The firing sequence applicable to the proposed synthsis algorithm is allowed to have repetitive appearances of the same transition and partial parallel firing sequences which do not contain the same transition in common, in other word, are independent each other. The synthesis algorithm consists of the following steps. (1) Connect the transitions to each other by places and arcs in the order of the given firing sequence. (2) Find out conflicts in the path, and if exist, prescribe the firing order among the conflicting transitions depending on the given specification. (3) For each conflict, make a path for the prescribed firing order by the same way as (1), and add it to the former graph. (4) Find out conflicts in the paths added at (3) , if exist, prescribe the firing order and back to (3) again. By repeating them until there exists no conflict, a Petri net which generates a given firing sequence is completed. The algorithm is executed by a computer, and we confirmed by simulation that a wellbehaved Petri net is synthesized.
doi:10.9746/sicetr1965.21.277 fatcat:orsotbkjtzdkxpofnfwycfpncq