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The properties of working set size strings, i.e., of the strings of integers representing the sequences of values taken by the working set sizes of programs, are investigated. Particular attention is given to the conditions to be satisfied by a given string of integers, by a pair of such strings, or by an n-tuple of strings for the existence of a page reference string whose working set size strings coincide with the given ones for given values of the window size. These conditions are useful in generating artificial reference strings exhibiting a given memory demand dynamics.

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