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Summary: Generalized Conditions for Liveness
Enforcement and Deadlock Prevention in Petri
Nets
Marian V. Iordache and Panos J. Antsaklis1
Department of Electrical Engineering, University of Notre Dame, Notre Dame,
IN46556 (e-mail: iordache.1, antsaklis.1@nd.edu)
Submitted as a theory paper
Abstract. This paper presents new results concerned with liveness, live-
ness 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.
Keywords liveness, deadlock, synthesis of liveness supervisors, struc-
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