References
V. M. Glushkov, Synthesis of Digital Automata [in Russian], Fizmatgiz, Moscow (1962).
V. M. Glushkov, Yu. V. Kapitonova, and A. T. Mishchenko, Discrete Logic Design [in Russian], Naukova Dumka, Kiev (1987).
A. D. Zakrevskii, Cascade Logic Design [in Russian], Nauka, Moscow (1981).
D. A. Pospelov, Logic Methods of Circuit Analysis and Design [in Russian], Énergiya, Moscow (1974).
B. G. Fedorkov and V. A. Telets, DAC and ADC Microcircuits: Operation, Parameters, Application [in Russian], Énergoatomizdat, Moscow (1990).
G. P. Gavrilov and A. A. Sapozhenko, Collection of Problems in Discrete Mathematics [in Russian], Nauka, Moscow (1977).
S. S. Marchenkov and A. B. Ugol'nikov, Closed Classes of Boolean Functions [in Russian], Inst. Prikl. Matem. Akad. Nauk SSSR, Moscow (1990).
S. V. Yablonskii, "Functional constructions ink-valued logic," Tr. Matem. Inst. im. V. A. Steklova, vol. 51, 2–142 (1958).
S. V. Yablonskii, An Introduction to Discrete Mathematics [in Russian], Nauka, Moscow (1979).
L. B. Avgul’ and V. P. Suprun, "Decomposition of Boolean functions using polynomial expansion," Izv. Akad. Nauk SSSR, Tekhn. Kibern., No. 3, 187–191 (1989).
L. B. Avgul’ and V. P. Suprun, "Generalized polynomial expansions of symmetrical Boolean functions," Kibernetika, No. 1, 122–125 (1991).
G. S. Avsarkisyan and G. S. Brailovskii, "Representation of logical functions in Zhegalkin polynomial form," Avtomat. i Vychisl. Tekhn., No. 6, 6–10 (1975).
V. P. Suprun, "Polynomial expansions of symmetrical Boolean functions," Izv. Akad. Nauk SSSR, Tekhn. Kibern., No. 4, 123–127 (1985).
V. P. Suprun, "Tabular method for polynomial expansion of Boolean functions," Kibernetika, No. 1, 116–117 (1987).
V. P. Suprun, "A method of polynomial expansion of Boolean functions," Kibernetika, No. 5, 122–124 (1989).
Zh. Toshich, "Polynomial representations of Boolean functions and their minimization," Izv. Akad. Nauk SSSR, Tekhn. Kibern., No. 3, 141–143 (1967).
S. Even, I. Kohavi, and A. Paz, "On minimal modulo-2 sums of products for switching functions," IEEE Trans. Electron. Comput.,16, No. 10, 671–674 (1967).
D. E. Muller, "Application of Boolean algebra to switching circuit design and error detection," IRE Trans. Electron. Comput.,3, No. 3, 6–12 (1954).
I. S. Reed, "A class of multiple-error-correcting codes and decoding scheme," IRE Trans. Inform. Theory,4, No. 9, 38–49 (1954).
E. K. Machikenas and V. P. Suprun, On Polynomial Expansion of Boolean Functions [in Russian], Unpublished manuscript, VINITI 09.03.88, No. 1899-V88.
G. S. Avsarkisyan, "Representation of Boolean functions by modulo-2 sum of implications of arguments," Avtomat. i Vychisl. Tekhn., No. 1, 8–11 (1977).
G. S. Avsarkisyan, "Generalized polynomial forms of Boolean functions and multioutput logic design," Avtomat. Telemekh., No. 11, 111–119 (1983).
G. S. Avsarkisyan, "Polynomial forms of partial Boolean functions and some applications," Izv. Akad. Nauk SSSR, Tekhn. Kibern., No. 5, 50–58 (1983).
G. S. Avsarkisyan, "Recursive polynomial forms of partial Boolean functions," Izv. Akad. Nauk SSSR, Tekhn. Kibern., No. 4, 131–135 (1987).
S. F. Vinokurov and N. A. Peryazev, "Polynomial expansions of Boolean functions by nondegenerate functions," Algebra i Logika,30, No. 6, 631–637 (1991).
S. F. Vinokurov and N. A. Peryazev, "Representation of Boolean functions by polynomial forms," Kibernetika i Sistemnyi Analiz, No. 3, 175–178 (1992).
S. F. Vinokurov and N. A. Peryazev, "Polynomial decomposition of Boolean functions," Mat. Zametki,30, No. 2, 25–29 (1993).
S. F. Vinokurov, Polynomial Operator Expansions and Canonical Forms of Boolean Functions [in Russian], preprint, Izd. Irkutsk. Univ. (1992).
G. P. Gavrilov, Functional Systems in Discrete Mathematics [in Russian], Izd. MGU, Moscow (1985).
V. A. Gorbatov, Fundamentals of Discrete Mathematics [in Russian], Vysshaya Shkola, Moscow (1986).
S. V. Yablonskii and O. B. Lupanov, eds., Discrete Mathematics and Mathematical Topics in Cybernetics [in Russian], vol. 1, Nauka, Moscow (1974).
S. V. Yablonskii, G. P. Gavrilov, and V. B. Kudryavtsev, Boolean Functions and Post Classes [in Russian], Nauka, Moscow (1966).
D. Bochmann and H. Posthof, Binary Dynamic Systems [Russian translation], Énergoatomizdat, Moscow (1986).
S. F. Vinokurov and N. A. Peryazev, "Polynomial expansions of Boolean functions," International Conference on Algebra in Memory of A. I. Shirshov, abstracts of papers in logic [in Russian], Barnaul (1991), p. 25.
S. J. Akers, "On theory of Boolean functions," J. SIAM,7, No. 4, 487–498 (1959).
G. E. Tseitlin, "Realization of Boolean functions in algebra with the system of operations &, −, +(mod 2)," in: Seminar on Automata Theory [in Russian], No. 3, Naukova Dumka, Kiev (1966), pp. 84–92.
M. Davio, "Taylor expansions of symmetric Boolean functions," Philips Res. Reports,28, 466–474 (1973).
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Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 34–47, November–December, 1993.
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Vinokurov, S.F., Peryazev, N.A. Polynomial expansions of Boolean functions. Cybern Syst Anal 29, 809–821 (1993). https://doi.org/10.1007/BF01122733
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DOI: https://doi.org/10.1007/BF01122733