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T-Liveness Enforcement in Petri Nets Based on Structural Net Properties

Summary: T-Liveness Enforcement in Petri Nets
Based on Structural Net Properties
Marian V. Iordache and Panos J. Antsaklis
We introduce a semidecidable procedure which, given a Petri net structure and a set T
of transitions, synthesizes a supervisor enforcing the transitions in T to be live. We call this
liveness property T -liveness. When T equals the total set of Petri net transitions, T -liveness
corresponds to liveness. Enforcing only a subset of transitions to be live is useful when some
Petri net transitions model undesired events such as failures, and/or when the Petri net structure
does not allow enforcing all transitions to be live. Our procedure is based on structural net
properties, and so the synthesized supervisors are independent of the initial marking. The
supervisors are least restrictive for a wide class of Petri nets. No assumptions are made on the
Petri net structure: the Petri nets may be unbounded and have integer weights. In this paper
we restrict our attention to fully controllable and observable Petri nets. However we note that
the procedure is rather easily extendable to Petri nets having uncontrollable and unobservable
1 Introduction
Petri nets are a compact representation of concurrent discrete event systems. One of the difficult
problems in the study of Petri nets is liveness. Liveness means that regardless of the current state


Source: Antsaklis, Panos - Department of Electrical Engineering, University of Notre Dame


Collections: Engineering