Detection of combined occurrences

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Abstract
In this paper it is supposed that the variables x 1 , … , x n each have finite range with the variable x i taking on p i possible values and that the values of the variables are changing with time. It is supposed further that it is desired to detect occurrences in which some subset of the variables achieve particular values. Finally, it is supposed that the problem involves the detection of a large number of combined occurrences for a large number of changes of values of variables. Two efficient solutions for this problem are described. Both methods have the unusual property of being faster for systems where the sum p 1 + … + p n is larger. The first solution is error-free and suitable for most cases. The second solution is slightly more elegant and allows negation as well as conjunction, but is subject to the possibility of errors. An error analysis is given for the second method and an empirical study is reported.

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