Abstract
The following problem is considered: Find Boolean function f of n variables with the property that, given any polynomial p of degree at most s, there exists a set of n-tuples such that p is the only polynomial of degree at most s taking the same values as f at these n-tuples. It is shown that for any fixed s and sufficiently large n, such a function exists and can be chosen from among those with domains of cardinality that grow as O(n s).
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Original Russian Text © A.A. Voronenko, 2017, published in Vestnik Moskovskogo Universiteta, Seriya 15: Vychislitel’naya Matematika i Kibernetika, 2017, No. 3, pp. 36–38.
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Voronenko, A.A. Universal functions for classes of Boolean polynomials. MoscowUniv.Comput.Math.Cybern. 41, 142–144 (2017). https://doi.org/10.3103/S0278641917030074
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DOI: https://doi.org/10.3103/S0278641917030074