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Polynomial expansions of Boolean functions

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References

  1. V. M. Glushkov, Synthesis of Digital Automata [in Russian], Fizmatgiz, Moscow (1962).

    Google Scholar 

  2. V. M. Glushkov, Yu. V. Kapitonova, and A. T. Mishchenko, Discrete Logic Design [in Russian], Naukova Dumka, Kiev (1987).

    Google Scholar 

  3. A. D. Zakrevskii, Cascade Logic Design [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  4. D. A. Pospelov, Logic Methods of Circuit Analysis and Design [in Russian], Énergiya, Moscow (1974).

    Google Scholar 

  5. B. G. Fedorkov and V. A. Telets, DAC and ADC Microcircuits: Operation, Parameters, Application [in Russian], Énergoatomizdat, Moscow (1990).

    Google Scholar 

  6. G. P. Gavrilov and A. A. Sapozhenko, Collection of Problems in Discrete Mathematics [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  7. S. S. Marchenkov and A. B. Ugol'nikov, Closed Classes of Boolean Functions [in Russian], Inst. Prikl. Matem. Akad. Nauk SSSR, Moscow (1990).

    Google Scholar 

  8. S. V. Yablonskii, "Functional constructions ink-valued logic," Tr. Matem. Inst. im. V. A. Steklova, vol. 51, 2–142 (1958).

    Google Scholar 

  9. S. V. Yablonskii, An Introduction to Discrete Mathematics [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  10. 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).

    Google Scholar 

  11. L. B. Avgul’ and V. P. Suprun, "Generalized polynomial expansions of symmetrical Boolean functions," Kibernetika, No. 1, 122–125 (1991).

    Google Scholar 

  12. G. S. Avsarkisyan and G. S. Brailovskii, "Representation of logical functions in Zhegalkin polynomial form," Avtomat. i Vychisl. Tekhn., No. 6, 6–10 (1975).

    Google Scholar 

  13. V. P. Suprun, "Polynomial expansions of symmetrical Boolean functions," Izv. Akad. Nauk SSSR, Tekhn. Kibern., No. 4, 123–127 (1985).

    Google Scholar 

  14. V. P. Suprun, "Tabular method for polynomial expansion of Boolean functions," Kibernetika, No. 1, 116–117 (1987).

    Google Scholar 

  15. V. P. Suprun, "A method of polynomial expansion of Boolean functions," Kibernetika, No. 5, 122–124 (1989).

    Google Scholar 

  16. Zh. Toshich, "Polynomial representations of Boolean functions and their minimization," Izv. Akad. Nauk SSSR, Tekhn. Kibern., No. 3, 141–143 (1967).

    Google Scholar 

  17. 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).

    Google Scholar 

  18. D. E. Muller, "Application of Boolean algebra to switching circuit design and error detection," IRE Trans. Electron. Comput.,3, No. 3, 6–12 (1954).

    Google Scholar 

  19. I. S. Reed, "A class of multiple-error-correcting codes and decoding scheme," IRE Trans. Inform. Theory,4, No. 9, 38–49 (1954).

    Google Scholar 

  20. E. K. Machikenas and V. P. Suprun, On Polynomial Expansion of Boolean Functions [in Russian], Unpublished manuscript, VINITI 09.03.88, No. 1899-V88.

  21. G. S. Avsarkisyan, "Representation of Boolean functions by modulo-2 sum of implications of arguments," Avtomat. i Vychisl. Tekhn., No. 1, 8–11 (1977).

    Google Scholar 

  22. G. S. Avsarkisyan, "Generalized polynomial forms of Boolean functions and multioutput logic design," Avtomat. Telemekh., No. 11, 111–119 (1983).

    Google Scholar 

  23. G. S. Avsarkisyan, "Polynomial forms of partial Boolean functions and some applications," Izv. Akad. Nauk SSSR, Tekhn. Kibern., No. 5, 50–58 (1983).

    Google Scholar 

  24. G. S. Avsarkisyan, "Recursive polynomial forms of partial Boolean functions," Izv. Akad. Nauk SSSR, Tekhn. Kibern., No. 4, 131–135 (1987).

    Google Scholar 

  25. S. F. Vinokurov and N. A. Peryazev, "Polynomial expansions of Boolean functions by nondegenerate functions," Algebra i Logika,30, No. 6, 631–637 (1991).

    Google Scholar 

  26. S. F. Vinokurov and N. A. Peryazev, "Representation of Boolean functions by polynomial forms," Kibernetika i Sistemnyi Analiz, No. 3, 175–178 (1992).

    Google Scholar 

  27. S. F. Vinokurov and N. A. Peryazev, "Polynomial decomposition of Boolean functions," Mat. Zametki,30, No. 2, 25–29 (1993).

    Google Scholar 

  28. S. F. Vinokurov, Polynomial Operator Expansions and Canonical Forms of Boolean Functions [in Russian], preprint, Izd. Irkutsk. Univ. (1992).

  29. G. P. Gavrilov, Functional Systems in Discrete Mathematics [in Russian], Izd. MGU, Moscow (1985).

    Google Scholar 

  30. V. A. Gorbatov, Fundamentals of Discrete Mathematics [in Russian], Vysshaya Shkola, Moscow (1986).

    Google Scholar 

  31. S. V. Yablonskii and O. B. Lupanov, eds., Discrete Mathematics and Mathematical Topics in Cybernetics [in Russian], vol. 1, Nauka, Moscow (1974).

    Google Scholar 

  32. S. V. Yablonskii, G. P. Gavrilov, and V. B. Kudryavtsev, Boolean Functions and Post Classes [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  33. D. Bochmann and H. Posthof, Binary Dynamic Systems [Russian translation], Énergoatomizdat, Moscow (1986).

    Google Scholar 

  34. 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.

  35. S. J. Akers, "On theory of Boolean functions," J. SIAM,7, No. 4, 487–498 (1959).

    Google Scholar 

  36. 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.

    Google Scholar 

  37. M. Davio, "Taylor expansions of symmetric Boolean functions," Philips Res. Reports,28, 466–474 (1973).

    Google Scholar 

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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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