Average Binary Long-Lived Consensus: Quantifying the Stabilizing Role Played by Memory

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 function f. This function returns, in each round, a representative output value v 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. The instability of the system is the number of output changes over a random sequence of input vectors. Our first result is to design optimal instability consensus systems with and without memory. Roughly, in the memoryless case, we show that an optimal system is D0, that outputs 1 unless it is forced by the faulttolerance requirement to output 0 (o...

• Type: Conference
• Year: 2008
• Where: SIROCCO
• Authors: Florent Becker, Sergio Rajsbaum, Ivan Rapaport, Eric Rémila
• Keywords: Information Technology, Input Vector, Representative Output Value, Sensor Readings, SIROCCO 2008