REFERENCES
V. B. Alekseev, “On decodingof some classes of monotone multivalued functions,” Zh.Vychisl.Mat.Mat.Fiz., 16, No. 1, 189–198 (1976).
V. B. Alekseev, “On the number of monotone k-valued functions,” Probl.Kibern., 28, 5–24 (1974).
G. Ansel, “On the number of monotone Boolean functions of n variables,” in: Cybernetical Collection, New Ser. 5 [Russian translation], Mir, Moscow (1968), pp. 53–57.
Yu. I. Zhuravlev, “On the algebraic approach to pattern recognition and the classi.cation problem,” Probl.Kibern., 33, 5–68 (1978).
Yu. I. Zhuravlev, S. N. Miroshnik, and S. M. Shvartin, “On an approach to optimization in the class of parametric algorithms of pattern recognition,” Zh.Vychisl.Mat.Mat.Fiz., 16, No. 1, 209–218 (1976).
N. N. Katerinochkina, “The search for a maximal upper zero of a monotone function of Boolean algebra,” Dokl.Akad.Nauk SSSR, 224, No. 3, 557–560 (1975).
N. N. Katerinochkina, “The search for a maximal upper zero for a class of monotone functions of k-valued logic,” Dokl.Akad.Nauk SSSR, 234, No. 4, 746–749 (1977).
A. Yu. Kitaev, “On the approximate computation of the height of a maximal upper zero of a monotone Boolean function,” Mat.Zametki, 50, No. 1, 41–45 (1991).
D. Kleitman, “On the Dedekind problem: the number of monotone Boolean functions,” Cybernetical Collection, New Ser. 7 [Russian translation] Mir, Moscow (1970) pp. 43–52.
V. K. Korobkov, “On the monotone functions of Boolean logic,” Probl.Kibern., 13, 5–28 (1965).
V. K. Korobkov, “On some integer linear programming problems,” Probl.Kibern., 14, 297–299 (1965).
V. K. Korobkov, “Some generalizations of the problem of 'decoding' of monotone functions in the Boolean logic,” Diskret.Anal., 3, 19–25 (1965).
A. D. Korshunov, “On the number of monotone functions,” Probl.Kibern., 38, 5–108 (1981).
N. N. Kuzyurin, “On the approximate search for a maximal upper zero for the monotone functions of the k-valued logic,” Metody Diskretnogo Analiza v Reshenii Ekstremal'nykh Zadach, 33, 31–40 (1979).
A. A. Sapozhenko, “On the number of antichains in multilayer ranked sets,” Diskret.Mat., 1, No. 2, 110–128 (1989).
A. A. Sapozhenko, “On the number of antichains in ranked partially ordered sets,” Diskret.Mat., 1, No. 1, 74–93 (1989).
A. A. Sapozhenko, “On the search for a maximal upper zero of monotone functions on ranked partially ordered sets,” Zh.Vychisl.Mat.Mat.Fiz., 31, No. 12, 1871–1884 (1991).
A. V. Serzhantov, “Optimal algorithm for decoding some monotone functions,” Mat.Voprosy Kibern., 1, 223–233 (1988).
A. N. Smirnov, “On the complexity of a class of Boolean programming problems,” in: Communication in Applied Mathematics [in Russian], Computer Center, Russian Academy of Sciences, Moscow (1978), p. 10.
N. A. Sokolov, “On the optimal decodingof monotone functions of Boolean algebra,” Zh.Vychisl.Mat.Mat.Fiz., 22, No. 2, 449–461 (1982).
N. A. Sokolov, “Optimal decoding of monotone Boolean functions,” Zh.Vychisl.Mat.Mat.Fiz., 27, No. 12, 1878–1887 (1987).
N. A. Sokolov, “The search for a maximal upper zero for a class of monotone discrete functions,” Dokl.Akad.Nauk SSSR, 251, No. 5, 1077–1080 (1980).
N. A. Sokolov, “The search for a maximal upper zero for a class of monotone functions of finite valued logic,” Zh.Vychisl.Mat.Mat.Fiz., 21, No. 6, 1552–1565 (1981).
N. A. Sokolov, “Partial decodingof monotone Boolean functions,” Zh.Vychisl.Mat.Mat.Fiz., 23, No. 5, 1267–1271 (1983).
N. A. Sokolov, “Complexity of optimization on independence systems,” Dokl.Akad.Nauk SSSR, 299, No. 4, 821–824 (1988).
N. A. Sokolov, On the decodingp roblem of monotone Boolean functions,” in: Combinatorial Models and Methods, Vol. 2 [in Russian], Computer Center of the Russian Academy of Sciences, Moscow (1996), pp. 73–84.
N. A. Sokolov, “On the isomorphisms of lattices of order ideals,” in: Combinatorial Models and Methods, Vol. 2 [in Russian], Computer Center of the Russian Academy of Sciences, Moscow (1995), pp. 66–70.
N. A. Sokolov, “On the search for maximal half subsets of a finite set,” Abstracts of Papers, Mathematical Methods of Pattern Recognition (MMRO-7) [in Russian], Moscow Pedagogical State Univ., Moscow (1995), pp. 57–58.
N. A. Sokolov, “On the isomorphisms of some principal orders,” Diskret.Anal.Issled.Operatsii, 2, No. 3, 80–82 (1995).
N. A. Sokolov, “Oracle complexity of order optimization on the Boolean cube,” in: Combinatorial Models and Methods, Vol. 2 [in Russian], Computer Center of the Russian Academy of Sciences, Moscow (1996), pp. 85–90.
N. A. Sokolov, “On the coveringo f some subsets of layers of the Boolean cube,” in: Combinatorial Models and Methods, Vol. 2 [in Russian], Computer Center of the Russian Academy of Sciences, Moscow (1996), pp. 15–24.
R. Stanley, Computational Combinatorics [Russian translation], Mir, Moscow (1990).
D. Hausmann and B. Korte, “Lower bounds of the worst-case complexity of some oracle algorithms,” Discr.Math., No. 24, 261–276 (1978).
D. Hausmann, B. Korte, and T. A. Jenkins, “Worst case analysis of greedy-type algorithms for independence systems,” Math.Progr.Stud., No. 12, 120–131 (1980).
S.-T. Hu, Threshold Logic, University of California Press, Berkeley (1965).
B. Korte, “Approximative algorithms for discrete optimization problems,” Ann.Discr.Math., 4, 85–120 (1979).
R. A. Proctor, “Solution of two combinatorial problems with linear algebra,” Amer.Math.Monthly, 89, 721–734 (1982).
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Sokolov, N.A. Problems of Order Optimization. Journal of Mathematical Sciences 108, 131–149 (2002). https://doi.org/10.1023/A:1012709400447
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DOI: https://doi.org/10.1023/A:1012709400447