Abstract
We design and implement highly parallel algorithms that use light as the tool of computation. Our computational laboratory consists of an ordinary xerox machine supplied with a box of transparencies. Our most basic operation is the evaluation of a Boolean function at arbitrarily many truth settings simultaneously. We find the maximum in a list of n-bit numbers of arbitrary length using at most n xerox copying steps. We count the number of elements in a list of arbitrary length of subsets of a given n-element set simultaneously in O(n2) copying steps. We decide, for any graph having n vertices and m edges, whether a 3-coloring exists in at most 2n + 4m copying steps. For large instances of problems such as the 3-color problem, this solution method may require the production of transparencies that display challengingly high densities of information. Our ultimate purpose here is to give hand tested 'ultra-parallel' algorithmic procedures that may provide useful suggestions for future technologies using light.
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