A theory of coteries: mutual exclusion in distributed systems

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A coterie under a ground set U consists of subsets (called quorums) of U such that any pair of quorums intersect with each other. Nondominated (ND) coteries are of particular interest, since they are optimal in some sense. By assigning a Boolean variable to each element in U, a family of subsets of U is represented by a Boolean function of these variables. The authors characterize the ND coteries as exactly those families which can be represented by positive, self-dual functions. In this Boolean framework, it is proved that any function representing an ND coterie can be decomposed into copies of the three-majority function, and this decomposition is representable as a binary tree. It is also shown that the class of ND coteries proposed by D. Agrawal and A. El Abbadi (1989) is related to a special case of the above binary decomposition, and that the composition proposed by M.L. Neilsen and M. Mizuno (1992) is closely related to the classical Ashenhurst decomposition of Boolean functions. A number of other results are also obtained. The compactness of the proofs of most of these results indicates the suitability of Boolean algebra for the analysis of coteries. >

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