Average long-lived binary consensus: quantifying the stabilizing role played by memory. (English summary) Theoret. Comput. Sci. 411 (2010), no. 14-15, 1558–1566. Summary: “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. “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: D0 without memory, and D1 with memory. Then we quantify the gain factor due to memory by computing cn(t), the number of decision change
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