This is a preview of subscription content, log in via an institution to check access.
References
V. M. Glushkov, “Abstract automata theory,”Usp. Mat. Nauk,16, No. 5(101), 3–61.
D. Slepian, “The class of binary signal alphabets,” in:Theory of Message Transmission [Russian translations], Inostr. Lit., Moscow (1957), pp. 82–113.
P. Erdös and A. Renyi, “On random matrices,”Magyar Tud. Akad. Kutato Int. Kozl., No. 8, 455–461 (1963).
G. V. Balakin, “On random matrices,”Teor. Veroyatn. Primen.,12, No. 2, 346–353 (1967).
G. V. Balakin, “Distribution of the rank of random matrices over a finite field,”Teor. Veroyatn. Primen.,13, No. 4, 631–641 (1968).
I. N. Kovalenko, “On distribution of the rank of a random matrix,”Teor. Veroyatn. Primen.,17, No. 2, 354–359 (1972).
V. F. Kolchin,Systems of Random Equations [in Russian], Izd. MIÉM, Moscow (1988).
A. A. Levitskaya, “Limiting distributions of the rank of a random 0-1 matrix with a fixed number of ones in rows,”Dokl. Akad. Nauk UkrSSR, Ser. A, No. 8, 45–48 (1991).
I. N. Kovalenko, “A limiting theorem for determinants in the class of Boolean functions,”Dokl. Akad. Nauk SSSR,161, No. 3, 517–519 (1965).
I. N. Kovalenko, “Limiting distribution of the number of solutions of a random system of linear equations in the class of Boolean functions,”Teor. Veroyatn. Primen.,12, No. 1, 51–61 (1967).
I. N. Kovalenko, “Distribution of the rank for random 0-1 matrices,”Kibernetika, No. 5, 138–152 (1975).
I. N. Kovalenko and A. A. Levitskaya, “Limiting behavior of the number of solutions of a system of random linear equations over a finite field and a finite ring,”Dokl. Akad. Nauk SSSR,221, No. 4, 778–781.
I. N. Kovalenko and A. A. Levitskaya, “Limiting behavior of the number of solutions of a system of random linear equations over a finite field and a finite ring,”Teor. Veroyatn. Mat. Stat., No. 13, 70–83 (1977).
I. N. Kovalenko, A. A. Levitskaya, and M. N. Savchuk,Selected Problems of Probabilistic Combinatorics [in Russian], Naukova Dumka, Kiev (1986).
M. V. Kozlov, “The rank of matrices with random 0-1 elements,”Dokl. Akad. Nauk SSSR,169, No. 5, 1013–1016 (1966).
A. A. Levitskaya, “Invariance theorems for the limiting behavior of the number of solutions of a system of random linear equations over a finite ring,”Kibernetika, No. 2, 140–141 (1978).
A. A. Levitskaya, “Invariance theorems for systems of random linear equations over an arbitrary finite ring,”Dokl. Akad. Nauk SSSR,263, No. 2, 279–281 (1982).
A. A. Levitskaya, “Invariance theorems for the rank of a random 0-1 matrix with a fixed number of ones in the rows,”Dokl. Akad. Nauk UkrSSR, Ser. A, No. 9, 51–54 (1991).
V. I. Masol, “Extension of the invariance region for random 0-1 matrices,”Kibernetika, No. 3, 125–128 (1980).
A. A. Levitskaya, “Limiting theorems for a system of random linear equations over an arbitrary finite ring,” in:Probability Methods of Discrete Mathematics, Abstracts of papers at All-Union Conf., Petrozavodsk (1983), pp. 43–44.
A. A. Levitskaya, “Invariance theorems for systems of random linear equations over an arbitrary finite ring without left unity,”Dokl. Akad. Nauk UkrSSR, Ser. A, No. 9, 71–72 (1984).
A. A. Levitskaya, “Probability of consistency of a system of random linear equations over a finite ring,”Teor. Veroyatn. Primen.,30, No. 2, 339–350 (1985).
A. A. Levitskaya, “Invariance theorems for systems of random linear equations in finite Abelian groups,” in:Probability Methods in Discrete Mathematics, Abstracts of papers at All-Union Conf., Petrozavodsk (1988), pp. 56–57.
Additional information
Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 100–105, May–June, 1993.
Rights and permissions
About this article
Cite this article
Kovalenko, I.N., Levitskaya, A.A. Probabilistic properties of systems of random linear equations over finite algebraic structures. Cybern Syst Anal 29, 385–390 (1993). https://doi.org/10.1007/BF01125544
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01125544