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On the Complexity of Polynomial Recurrence Sequences

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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.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia

    S. S. Marchenkov

Authors
  1. S. S. Marchenkov
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Correspondence to S. S. Marchenkov.

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.

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Marchenkov, S.S. On the Complexity of Polynomial Recurrence Sequences. Probl Inf Transm 54, 258–262 (2018). https://doi.org/10.1134/S0032946018030055

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  • DOI: https://doi.org/10.1134/S0032946018030055

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