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On the structural computation of synchronic invariants in P/T nets.

Silva, M.; Colom, J.M.

In: Proceedings of the Eighth European Workshop on Application and Theory of Petri Nets, Zaragoza, Espana, pages 237-258. 1987.

Abstract: Inside Synchrony Theory, this paper deals with a structural computation of synchronic invariants. It is based on the state equation of the place/transition (P/T) net and on Linear Programming theory. The approach is conceptually very simple, general and computationally very efficient. It is said to be a general approach in the sense that instead of single transitions, subsets of transitions are directly taken into account. Computationally it is very efficient because the linear programming problem is know to be of polynomial complexity. Two transition subsets are in a given synchronic relation if the corresponding synchronic invariant is bounded; for any conflict-resolution strategies, synchronic relations characterize the existence or non-existence of firing dependences. As a by-product of the proposed approach, a full algebraic characterization of structural synchronic relations (i.e. independent of the initial marking) is obtained.

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