On the dimension of the solution space of linear difference equations over the ring of infinite sequences

Sergei Abramov; Gleb Pogudin

doi:10.1016/j.jsc.2024.102350

On the dimension of the solution space of linear difference equations over the ring of infinite sequences

Sergei Abramov
, Gleb Pogudin

Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

For a linear difference equation with the coefficients being computable sequences, we establish algorithmic undecidability of the problem of determining the dimension of the solution space including the case when some additional prior information on the dimension is available.

langue originale	Anglais
Numéro d'article	102350
journal	Journal of Symbolic Computation
Volume	127
Les DOIs	https://doi.org/10.1016/j.jsc.2024.102350
état	Publié - 1 mars 2025

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10.1016/j.jsc.2024.102350

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title = "On the dimension of the solution space of linear difference equations over the ring of infinite sequences",

abstract = "For a linear difference equation with the coefficients being computable sequences, we establish algorithmic undecidability of the problem of determining the dimension of the solution space including the case when some additional prior information on the dimension is available.",

keywords = "Linear difference operator with sequence coefficients, Solution space dimension, Undecidability",

author = "Sergei Abramov and Gleb Pogudin",

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AU - Abramov, Sergei

AU - Pogudin, Gleb

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N2 - For a linear difference equation with the coefficients being computable sequences, we establish algorithmic undecidability of the problem of determining the dimension of the solution space including the case when some additional prior information on the dimension is available.

AB - For a linear difference equation with the coefficients being computable sequences, we establish algorithmic undecidability of the problem of determining the dimension of the solution space including the case when some additional prior information on the dimension is available.

KW - Linear difference operator with sequence coefficients

KW - Solution space dimension

KW - Undecidability

U2 - 10.1016/j.jsc.2024.102350

DO - 10.1016/j.jsc.2024.102350

M3 - Article

AN - SCOPUS:85197367483

SN - 0747-7171

VL - 127

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

M1 - 102350

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On the dimension of the solution space of linear difference equations over the ring of infinite sequences

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