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On liveness analysis through linear algebraic techniques.

Colom, J.M.; Campos, J.; Silva, M.

In: Proceedings of Design Methods Based on Nets, Esprit Basic Research Action 3148, W.G. 6, Deliverables Covering the Period June 1989 to June 1990, Paris, France. 1990.

Abstract: Proving properties of Place/Transition Nets throught Linear Algebraic Techniques is very interesting because of the polynomial complexity of the algorithms used for this purpose. In this sense, many works have been devoted to the linear analysis of marking related properties (e.g. boundedness of the state space, mutual exclusions, etc.). Nevertheless, few results exist related to linear analysis of liveness properties. In this note, we investigate some applications of linear techniques to partial characterization of liveness properties. First, a necessary condition for structural liveness in structural bounded nets is presented. It is based on the rank of the incidence matrix. Finally, given an initial marking, some sufficient conditions for dead transitions and for deadlock-freeness are presented.

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