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On an undecidable problem related to difference equations with parameters

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Abstract

Linear difference equations with polynomial coefficients depending on parameters are considered. It is proved that the problem of existence of numerical values of parameters for which the given equation has a polynomial solution (alternatively, a solution given by a rational function) is undecidable (similar to the undecidability of the same problem in the differential case proved by J.-A. Weil).

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Authors and Affiliations

  1. Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

    S. A. Abramov

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  1. S. A. Abramov
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Correspondence to S. A. Abramov.

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Original Russian Text © S.A. Abramov, 2010, published in Programmirovanie, 2010, Vol. 36, No. 2.

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Abramov, S.A. On an undecidable problem related to difference equations with parameters. Program Comput Soft 36, 63–67 (2010). https://doi.org/10.1134/S0361768810020027

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  • DOI: https://doi.org/10.1134/S0361768810020027

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