On Liveness and Deadlockability in Subclasses of Weighted Petri Nets

Thomas Hujsa (1) , Raymond Devillers (2)

1 Department of Computing Science, Carl von Ossietzky Universität Oldenburg, D-26111 Oldenburg, Germany
2 ULB - Département d'Informatique [Bruxelles]

Structural approaches have greatly simplified the analysis of intractable properties in Petri nets, notably liveness. In this paper, we further develop these structural methods in particular weighted sub-classes of Petri nets to analyze liveness and deadlockability, the latter property being a strong form of non-liveness. For homogeneous join-free nets, from the analysis of specific substruc-tures, we provide the first polynomial-time characterizations of structural liveness and structural deadlockability, expressing respectively the existence of a live marking and the deadlockability of every marking. For the join-free class, assuming structural boundedness and leaving out the homogeneity constraint, we show that liveness is not monotonic, meaning not always preserved upon any increase of a live marking. Finally, we use this new material to correct a flaw in the proof of a previous characterization of monotonic liveness and boundedness for homogeneous asymmetric-choice nets, published in 2004 and left unnoticed.

Domaines: Systèmes embarqués

Thomas Hujsa, Raymond Devillers. On Liveness and Deadlockability in Subclasses of Weighted Petri Nets. 38th International Conference, PETRI NETS 2017, Zaragoza, Spain, June 25–30, 2017, Proceedings, pp.267-287, 2017. ⟨hal-02127837⟩