Marian V. Iordache and Panos J. Antsaklis
Proceedings of the 22nd International Conference on Application
and Theory of Petri Nets (ICATPN2001), Newcastle upon Tyne, UK,
25-29 June 2001.
Abstract -- This paper presents new results
concerned with liveness, liveness of a subset of transitions and
deadlock in Petri nets. Liveness is seen as a particular case of
what we call T-liveness: all transitions in the set T are live.
The first results characterize the relation between
supervisors enforcing liveness and T-liveness with supervisors
preventing deadlock. Then we introduce a class of Petri net
subnets allowing us to extend two well known results.
Specifically we generalize the result relating dead-lock to
siphons to a necessary and sufficient condition, and we extend
the recent generalization of Commoner's Theorem for asymmetric
choice Petri nets. We conclude by considering how the theoretical
results of this paper can be used for deadlock prevention, least
restrictive deadlock prevention and least restrictive T-liveness
enforcement.
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