Average long-lived binary consensus: Quantifying the stabilizing role played by memory

  • Authors:
  • Florent Becker;Sergio Rajsbaum;Ivan Rapaport;Eric Rémila

  • Affiliations:
  • Université de Lyon, Laboratoire de lInformatique du Parallélisme, UMR 5668 CNRS-ENS Lyon-Univ. Lyon 1, France;Instituto de Matemáticas, Universidad Nacional Autónoma de México (UNAM), México;Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (UMI 2807 CNRS), Universidad de Chile, Chile;Université de Lyon, Laboratoire de lInformatique du Parallélisme, UMR 5668 CNRS-ENS Lyon-Univ. Lyon 1, France

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2010

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Abstract

Consider a system composed of n sensors operating in synchronous rounds. In each round an input vector of sensor readings x is produced, where the i-th entry of x is a binary value produced by the i-th sensor. The sequence of input vectors is assumed to be smooth: exactly one entry of the vector changes from one round to the next one. The system implements a fault-tolerant averaging consensus functionf. This function returns, in each round, a representative output valuev of the sensor readings x. Assuming that at most t entries of the vector can be erroneous, f is required to return a value that appears at least t+1 times in x. We introduce the definition of instability of the system, which consists in the number of output changes over a random sequence of input vectors. We first design optimal (with respect to the instability measure) consensus systems: D"0 without memory, and D"1 with memory. Then we quantify the gain factor due to memory by computing c"n(t), the number of decision changes performed by D"0 per decision change performed by D"1.