The problem of random number generation datesudback to von Neumann's work in 1951. Since then, many algorithmsudhave been developed for generating unbiased bits fromudcomplex correlated sources as well as for generating arbitraryuddistributions from unbiased bits. An equally interesting, but lessudstudied aspect is the structural component of random numberudgeneration as opposed to the algorithmic aspect. That is, givenuda network structure imposed by nature or physical devices,udhow can we build networks that generate arbitrary probabilityuddistributions in an optimal way?ududIn this paper, we study the generation of arbitrary probabilityuddistributions in multivalued relay circuits, a generalization inudwhich relays can take on any of N states and the logicalud'and' and 'or' are replaced with 'min' and 'max' respectively.udPrevious work was done on two-state relays. We generalize theseudresults, describing a duality property and networks that generateudarbitrary rational probability distributions. We prove that theseudnetworks are robust to errors and design a universal probabilityudgenerator which takes input bits and outputs arbitrary binaryudprobability distributions.
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