The following problem is considered: specify a Boolean function of n variables such that every bilinear (polylinear) function is reduced, on a certain number of tuples of the specified function, to a unique bilinear (polylinear) function that is identical with the specified function on these tuples. We show that this is feasible for bilinear functions and for polylinear functions with a fixed number of parentheses k, starting with some n , and we can restrict the analysis to a sequence of functions with definition domain of cardinality O(n).
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A. A. Voronenko and M. N. Vyalyi, “Lower bound on the cardinality of the definition domain of universal functions for the class of linear Boolean functions,” Diskr. Mat., No. 4, 50–57 (2016); English translation: Discrete Mathematics and Applications, VSP (Netherlands), 27, No. 5, 319–324 (2017).
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Translated from Prikladnaya Matematika i Informatika, No. 57, 2018, pp. 84–86.
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Voronenko, A.A. Universal Functions for Classes of Bilinear and Polylinear Boolean Functions. Comput Math Model 29, 449–452 (2018). https://doi.org/10.1007/s10598-018-9423-4
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DOI: https://doi.org/10.1007/s10598-018-9423-4