Abstract
This paper considers some realization features of polynomial factoring algorithms for n-argument Boolean functions, as well as analyzes their computational complexity and necessary hardware resources.
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Hirayama, T., Nagasawa, K., Nishitani, Y., and Shimizu, K., Double Fixed-Polarity Reed-Muller Expressions: A New Class of AND-EXOR Expressions for Compact and Testable Realization, IPSJ, 2001, vol. 42, no. 4, pp. 983–991.
Akinina, J.S. and Tyurin, S.V., An Alternative Approach to Testability of Two-Level User-Programmable Logical Matrices, Vestn. Voronezh. Gos. Tekh. Univ., 2003, vol. 8.3, pp. 32–35.
Akinina, J.S., Podval’nyi, S.L., and Tyurin, S.V., Method of Testable Realisation of Logical Converters, RF Patent 2413282, Bull. Izobret., 2011, no. 6.
Zhegalkin, I.I., The Technique of Calculation of Statements in Symbolic Logic, Mat. Sb., 1927, vol. 34, pp. 9–28.
Zakrebskii, A.D. and Toropov, N.R., Polinomial’naya realizatsiya chastichnykh bulevykh funktsii i sistem (Polynomial Realization of Partial Boolean Functions and Systems), Moscow: Editorial URSS, 2003.
Akinin, A.A., Akinina, J.S., Podval’nyi, S.L., and Tyurin, S.V., Automatization of the Polynomial Distortion of Boolean Functions Based on the Method of Indefinite Coefficients, Sist. Upravlen. Inf. Tekhn., 2011, no. 2(44), pp. 4–8.
Akinin, A.A., Akinina, J.S., and Tyurin, S.V., Boolean Function Polynomial Factoring Computerization Based on Finite-Difference Technique, Sist. Upravlen. Inf. Tekhn., 2011, no. 4(46), pp. 69–73.
Akinin, A.A., An Algorithm of the Fractal Polynomial Factoring of Boolean Functions, Vestn. Voronezh. Gos. Tekh. Univ., 2011, vol. 7, no. 11, pp. 85–88.
Akinin, A.A., Polynomial Factoring Computerization for Boolean Functions by the Method of Fractal Transformations, Tr. V mezhd. konf. “Intellektual’nyi potentsial molodykh uchenykh Rossii i zarubezh’ya” (Proc. V Int. Conf. “Intellectual Potential of Young Scientists of Russia and Foreign Countries”), Moscow: Sputnik+, 2012, pp. 9–18.
Akinin, A.A., Akinina, Yu.S., and Tyurin, S.V., Method for Binary and Vector Polynomial Factoring of Boolean Functions, Proc. All-Russia Sci. Tech. Conf. Problems of Advanced Micro- and Nanoelectronic System Development, Moscow: IPPM, 2012, pp. 55–60.
Podval’nyi, S.L., Multi-Alternative Systems: Review Classification, Sist. Upravlen. Inf. Tekhn., 2012, no. 2(48), pp. 4–13.
Matematicheskaya entsiklopediya (Encyclopedia of Mathematics), Vinogradov, I.M., Ed., Moscow: Sovetskaya Entsiklopediya, 1977, vol. 1 (A-G).
Krinitskii, N.A., Ravnosil’nye preobrazovaniya algoritmov i programmirovanie (Equivalence Transformations of Algorithms and Programming), Moscow: Sovetskoe Radio, 1970.
Gavrilov, G.P. and Sapozhenko, A.A., Zadachi i uprazhneniya po diskretnoi matematike (Problems and Exercises in Discrete Mathematics), Moscow: Fizmatlit, 2005.
Gorbatov, V.A., Gorbatov, A.V., and Gorbatova, M.V., Teoriya avtomatov (Automata Theory), Moscow: AST, Astrel’, 2008.
Bochmann, D. and Posthoff, C., Binäre dynamische Systeme, Wien: Oldenburg, 1981. Translated under the title Dvoichnye dinamicheskie sistemy, Moscow: Energoatomizdat, 1986.
Matematicheskaya entsiklopediya (Encyclopedia of Mathematics), Vinogradov, I.M., Ed., Moscow: Sovetskaya Entsiklopediya, 1979, vol. 2 (D-K).
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Original Russian Text © A.A. Akinin, A.V. Achkasov, S.L. Podval’nyi, S.V. Tyurin, 2013, published in Sistemy Upravleniya i Informatsionnye Tekhnologii, 2013, No. 3, pp. 108–112.
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Akinin, A.A., Achkasov, A.V., Podval’nyi, S.L. et al. Polynomial transformation of Boolean functions: Analysis of computational algorithms. Autom Remote Control 75, 1301–1308 (2014). https://doi.org/10.1134/S0005117914070108
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DOI: https://doi.org/10.1134/S0005117914070108