The choice coordination problem

In the course of a concurrent computation, processes P1,..., Pn must reach a common choice of one out of k alternatives A₁,..., A_k. They do this by protocols using k shared variables, one for each alternative. If the range of the variables has m values then {Mathematical expression} is necessary, and n + 2≦m is sufficient, for deterministic protocols solving the choice coordination problem (C.C.P.). We introduce very simple randomizing protocols which, independently of n, solve the C.C.P. by use of a fixed alphabet. A single-byte (256-valued) alphabet permits a solution with non-termination probability smaller than 2^-127. Many software and hardware tasks involving concurrency can be interpreted as choice coordination problems. Choice coordination problems occur also in nature.