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

Silva, M.;
Colom, J.M.
In:
Rozenberg, G.: *Lecture Notes in Computer Science, Vol. 340: Advances in Petri Nets 1988*, pages 386-417.
Springer-Verlag,
1988.

Abstract:
Inside Synchrony Theory, this paper deals with a computation of structural
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 known to be of polynomial complexity. Two transition subsets
are in a given synchronic relation if the corresponding synchronic
invariant is bounded; for all 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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