Abstract
The computation complexity of a ternary linear function of n variables is found to be at least \(n^2 + \tfrac{3} {2}n - o(n)\).
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S. V. Avgustinovich, Yu. L. Vasil’ev, and K. L. Rychkov, “Computation Complexity of a Ternary Linear Function,” Diskret. Anal. Isled. Oper. 19(3), 3–12 (2012) [J. Appl. Indust. Math. 6 (4), 403–409 (2012)].
G. P. Gavrilov and A. A. Sapozhenko, Problems and Exercises in Discrete Mathematics (Fizmatlit, Moscow, 2005) [in Russian].
K. L. Rychkov, “A Modification of V. M. Khrapchenko’s Method and Its Application to the Complexity Estimates of π-Circuits for Code Functioins,” Diskretn. Anal. 42, 91–98 (1985).
K. L. Rychkov, “On Lower Bounds for the Complexity of Parallel-Serial Contact Circuits Realizing Linear Boolean Functions,” Sibirsk. Zh. Issled. Oper. 1(4), 33–52 (1994).
K. L. Rychkov, “On Complexity of Generalized Contact Circuits,” Diskretn. Anal. Isled. Oper. 16(5), 78–87 (2009).
K. L. Rychkov, “A Lower Bound for the Computation Complexity of a q-Ary Counter of Multiplicity Q in the Class of π-Circuits,” Diskretn. Anal. Isled.Oper. 17(6), 68–76 (2010) [J. Appl. Indust.Math. 5 (2), 290–295 (2011)].
V. M. Khrapchenko, “Complexity of the Realization of a Linear Function in the Class of π-Circuits,” Mat. Zametki 9(1), 35–40 (1971) [Math. Notes Acad. Sci. USSR 9 (1), 21–23 (1971)].
V. M. Khrapchenko, “Method of Determining Lower Bounds for the Complexity of π-Schemes,” Mat. Zametki 10(1), 83–92 (1971) [Math. Notes Acad. Sci. USSR 10 (1), 474–479 (1971)].
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Original Russian Text © Yu.L. Vasil’ev, K.L. Rychkov, 2013, published in Diskretnyi Analiz i Issledovanie Operatsii, 2013, Vol. 20, No. 4, pp. 15–26.
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Vasil’ev, Y.L., Rychkov, K.L. A lower estimate for the computation complexity of a ternary linear function. J. Appl. Ind. Math. 7, 588–596 (2013). https://doi.org/10.1134/S1990478913040133
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DOI: https://doi.org/10.1134/S1990478913040133