This paper continues the authors' previous work on studying the communication among decentralized supervisors for a distributed Discrete-Event System (DES) in the framework of Distributed Supervised DES (DSDES). Given an already available centralized supervisor for a distributed DES, it relates a language property of this supervisor, called weak joint observability, to a property of the state-based realization of the supervisor, referred to as the existence of the Independent Updating Functions (IUFs). The latter property means that the decentralized implementation of the supervisor relies on each agent's independent observation of the DES dynamic evolution and entails simpler, delay-robust, and possibly cheaper communication; issues currently under investigation. Examples illustrate the applicability of the approach.
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