Undecidable problems of decentralized observation and control on regular languages

  • Authors:
  • Stavros Tripakis

  • Affiliations:
  • VERIMAG--C.N.R.S., Centre Equation, 2, avenue de Vignate, 38610 Gières, France

  • Venue:
  • Information Processing Letters
  • Year:
  • 2004

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Abstract

We introduce a decentralized observation problem, where the system under observation is modeled as a regular language L over a finite alphabet Σ and n subsets of Σ model distributed observation points. A regular language K ⊆ L models a set of distinguished behaviors, say, correct behaviors of the system. The objective is to check the existence of a function which, given the n observations corresponding to a behavior ρ ∈ L, decides whether ρ is in K or not. We prove that checking the existence of such a function is undecidable. We then use this result to show undecidability of a decentralized supervisory control problem in the discrete event system framework.