Wielomianowy algorytm wyznaczania hipergrafu współbieżności w sieciach Petriego swobodnego wyboru

W referacie zaproponowano metodę umożliwiającą określenie strukturalnej relacji współbieżności w sieciach Petriego swobodnego wyboru (Free Choice). Algorytm znajduje miejsca wzajemnie współbieżne na podstawie struktury sieci oraz miejsc oznaczonych markerem startowym. W odróżnieniu od istniejących algorytmów, proponowana metoda znajduje wszystkie miejsca wzajemnie współbieżne, wyznaczając hipergraf współbieżności. Przeprowadzone badania eksperymentalne potwierdzają bardzo wysoką skuteczność proponowanej metody.

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In the paper a new algorithm of concurrency hypergraph computation is presented. The main aim of the proposed method is computation of a concurrency hypergraph in the polynomial time. The algorithm input is specified by the Petri net that belongs to the Free Choice subclass. Based on the net structure, the method outputs the concurrency relations between all places in the net. Particular relations are stored by the concurrency hypergraph instead of the concurrency graph, which is currently practiced. The hypergraph permits to store information about relations between all places in the net. In case of the concurrency graph it is limited to relations between pairs of places. Therefore, application of the concurrency hypergraph seems to be more intuitive and natural. The algorithm bases on the traditional solutions, however particular concurrency relation may contain more than two places which is not possible in currently known methods. The proposed solution is especially valuable in combination with the method presented in [1, 2] and permits to find the subsequent SM-Components in the polynomial time. The algorithm was experimentally verified. The method was compared with the traditional solution, where all maximal cliques in the concurrency graph were computed. The obtained results proved very high effectiveness of the proposed algorithm, which was always better than methods based on the graph theory. We have also noticed that the effectiveness increases drastically with the number of places and transitions in the Petri net.