Problems of Information Transmission

, Volume 54, Issue 3, pp 258–262 | Cite as

On the Complexity of Polynomial Recurrence Sequences

  • S. S. MarchenkovEmail author
Automata Theory


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.


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  1. 1.
    Hall, M., Jr., Combinatorial Theory, Waltham: Blaisdell, 1967. Translated under the title Kombinatorika, Moscow: Mir, 1970.Google Scholar
  2. 2.
    Nechaev, V.I., Elementy kriptografii: osnovy teorii zashchity informatsii (Elements of Cryptography: Basics of Information Protection Theory), Moscow: Vyssh. Shkola, 1999.Google Scholar
  3. 3.
    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].MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Minsky, M.L., Computation: Finite and Infinite Machines, Englewood Cliffs, NJ: Prentice-Hall, 1967. Translated under the title Vychisleniya i avtomaty, Moscow: Mir, 1971.Google Scholar
  5. 5.
    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.zbMATHGoogle Scholar

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© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Faculty of Computational Mathematics and CyberneticsLomonosov Moscow State UniversityMoscowRussia

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