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We consider synchronous distributed systems in which anonymous processorscommunicate by shared read-write variables. The goal is to have all theprocessors assign unique names to themselves. We consider the instances of thisproblem determined by whether the number $n$ is known or not, and whetherconcurrently attempting to write distinct values into the same memory cell isallowed or not, and whether the number of shared variables is a constantindependent of $n$ or it is unbounded. For known $n$, we give Las Vegasalgorithms that operate in the optimum expected time, as determined by theamount of available shared memory, and use the optimum $O(n\log n)$ expectednumber of random bits. For unknown $n$, we give Monte Carlo algorithms thatproduce correct output upon termination with probabilities that are$1-n^{-\Omega(1)}$, which is best possible when terminating almost surely andusing $O(n\log n)$ random bits.

Anonymous Processors with Synchronous Shared Memory