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English version: Journal of Applied and Industrial Mathematics, 2017, 11:4, 545-553 |
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Volume 24, No 4, 2017, P. 60-76 UDC 519.716
Keywords: bounded suffix summation, bounded suffix multiplication. DOI: 10.17377/daio.2017.24.558 Sergey S. Marchenkov 1 Received 30 November 2016 References[1] S. A. Volkov, An example of a simple quasi-universal function in the class $\mathscr E^2$ of the Grzegorczyk hierarchy, Diskretn. Mat., 18, No. 4, 31–44, 2006 [Russian]. Translated in Discrete Math. Appl., 16, No. 5, 513–526, 2006.[2] A. I. Maltsev, Iterative algebras and Post manifolds, Algebra Logika, 5, No. 2, 5–24, 1966 [Russian]. [3] A. I. Maltsev, Iterativnye algebry Posta (Iterative Post Algebras), Izd. NGU, Novosibirsk, 1976 [Russian]. [4] S. S. Marchenkov, Elimination of recursion schemas in the Grzegorczyk class $\mathscr E^2$, Mat. Zamet., 5, No. 5, 561–568, 1969 [Russian]. Translated in Math. Notes Acad. Sci. USSR, 5, No. 5, 336–340, 1969. [5] S. S. Marchenkov, On bounded recursions, Math. Balk., 2, 124–142, 1972 [Russian]. [6] S. S. Marchenkov, Bases under superposition in the classes of recursive functions, Matematicheskie voprosy kibernetiki (Mathematical Problems of Cybernetics), Vol. 3, pp. 115–139, Nauka, Moscow, 1991 [Russian]. [7] S. S. Marchenkov, Superpositions of elementary arithmetical functions, Disret. Anal. Issled. Oper., 13, No. 4, 33–48, 2006 [Russian]. Translated in J. Appl. Ind. Math., 1, No. 3, 351–360, 2007. [8] S. S. Marchenkov, Elementarnye arifmeticheskie funktsii (Elementary Arithmetical Functions), LIBROKOM, Moscow, 2009 [Russian]. [9] S. S. Marchenkov, Bounded monotonic recursion and multihead automata, Program., No. 6, 3–11, 2013 [Russian]. Translated in Program. Comput. Softw., 39, No. 6, 301–308, 2013. [10] S. S. Marchenkov, On elementary word functions obtained by bounded prefix concatenation, Diskretn. Mat., 27, No. 3, 44–55, 2015 [Russian]. Translated in Discrete Math. Appl., 26, No. 3, 155–163, 2016. [11] S. S. Marchenkov, Klassy elementarnykh rekursivnykh funktsii (Classes of Elementary Recursive Functions), FIZMATLIT, Moscow, 2016 [Russian]. [12] K. V. Osipov, On quasi-universal word functions Vestn. Mosk. Univ., Ser. 15, No. 1, 28–34, 2016 [Russian]. Translated in Mosc. Univ. Comput. Math. Cybern., 40, No. 1, 28–34, 2016. [13] L. Kalmár, Egyszerü példa eladönthetetlen aritmetikai problémára, Mat. Fiz. Lapok, 50, 1–23, 1943 [Hungarian]. |
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