A Strict Minimal Siphon-Based Necessary and Sufficient Condition for Liveness Verification in General Petri Nets

A Strict Minimal Siphon-Based Necessary and Sufficient Condition for Liveness Verification in General Petri Nets

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To describe deadlocks occurring in general nets, some characterizations have been proposed to establish a relationship dea eyewear between liveness and siphons.Among them, the most prominent characterizations are max-controlled siphons and deadly marked siphons.Nevertheless, the former is only a sufficient condition while the latter may lead to some unreasonable operations, i.e.

, modified markings are necessary if applicable.In this paper, we elaborately discuss the related concepts of deadly marked siphons when liveness analysis is conducted.Subsequently, a new siphon-based characterization of liveness, i.e.

, undermarked siphons that explain liveness in the original markings, is proposed to jilungin dreaming tea demonstrate its more general applicability.Finally, a necessary and sufficient condition is developed to show the relationship between the liveness and undermarked siphons in general nets.