Abstract
We consider recurrence sequences over the set of integers with generating functions being arbitrary superpositions of polynomial functions and the sg function, called polynomial recurrence sequences. We define polynomial-register (PR) machines, close to random-access machines. We prove that computations on PR machines can be modeled by polynomial recurrence sequences. On the other hand, computation of elements of a polynomial recurrence sequence can be implemented using a suitable PR machine.
Similar content being viewed by others
References
Hall, M., Jr., Combinatorial Theory, Waltham: Blaisdell, 1967. Translated under the title Kombinatorika, Moscow: Mir, 1970.
Nechaev, V.I., Elementy kriptografii: osnovy teorii zashchity informatsii (Elements of Cryptography: Basics of Information Protection Theory), Moscow: Vyssh. Shkola, 1999.
Marchenkov, S.S., On the Complexity of Recurring Sequences, Diskret. Mat., 2003, vol. 15, no. 2, pp. 52–62 [Discrete Math. Appl. (Engl. Transl.), 2003, vol. 13, no. 2, pp. 167–178].
Minsky, M.L., Computation: Finite and Infinite Machines, Englewood Cliffs, NJ: Prentice-Hall, 1967. Translated under the title Vychisleniya i avtomaty, Moscow: Mir, 1971.
Aho, A.V., Hopcroft, J.E., and Ullman, J.D., The Design and Analysis of Computer Algorithms, Reading: Addison-Wesley, 1976. Translated under the title Postroenie i analiz vychislitel’nykh algoritmov, Moscow: Mir, 1979.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © S.S. Marchenkov, 2018, published in Problemy Peredachi Informatsii, 2018, Vol. 54, No. 3, pp. 67–72.
Supported in part by the Russian Foundation for Basic Research, project no. 16-01-00593.
Rights and permissions
About this article
Cite this article
Marchenkov, S.S. On the Complexity of Polynomial Recurrence Sequences. Probl Inf Transm 54, 258–262 (2018). https://doi.org/10.1134/S0032946018030055
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0032946018030055