Universal functions for linear functions depending on two variables
-
Andrey A. Voronenko
and
Anna S. Okuneva
Abstract
We consider universal function’s construction for classes of sums of two arguments modulo 2. We constructed functions with optimal domain cardinality O(log n).
Originally published in Diskretnaya Matematika (2020) 32, №1, 3–7 (in Russian).
Funding source: Russian Science Foundation
Award Identifier / Grant number: 16-11-10014
Funding statement: This research was carried out with the support of the Russian Science Foundation (grant no. 16-11-10014)
References
[1] Voronenko A.A., “On universal functions for the set of linear functions”, Discrete Math. Appl., 22:4 (2012), 421–425.10.1515/dma-2012-028Search in Google Scholar
[2] Voronenko A.A., Vyalyi M.N., “Lower estimate of the cardinality of the domain of the universal functions for the class of linear Boolean functions”, Discrete Math. Appl., 27:5 (2017), 319–324.10.1515/dma-2017-0033Search in Google Scholar
[3] Voronenko A.A., Karchmit I.A., “Refining the upper bound for the cardinality of the definition domain of universal functions for a class of linear Boolean functions”, Moscow Univ. Comput. Math. Cyber., 2019,№4, 196–197.10.3103/S0278641919040095Search in Google Scholar
[4] Tokareva N.N., Nonlinear Boolean functions: bent functions and their generalizations, LAP LAMBERT Academic Publishing, Saarbrucken, Germany, 2011, 180 pp.Search in Google Scholar
[5] Zhuravlev Yu.I., Flerov Yu.A., Vyalyy M.N., Diskretnyi analiz. Osnovy vysshei algebry, MZ Press, Moscow, 2007 (in Russian), 224 pp.Search in Google Scholar
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Articles in the same Issue
- Attribute-efficient learning of Boolean functions from Post closed classes
- Easily testable circuits in Zhegalkin basis in the case of constant faults of type “1” at gate outputs
- Post theorem for strongly dependent n-ary semigroups
- Effective parallelization strategy for the solution of subset sum problems by the branch-and-bound method
- On the number of ones in outcome sequence of extended Pohl generator
- The number of sumsets in Abelian group
- Generalized allocation scheme with cell occupancies from a fixed finite set
- Universal functions for linear functions depending on two variables
