On polynomial-modular recursive sequences
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Sergey S. Marchenkov
Abstract
We consider recursive sequences over the set of integers, where as rules of generation we take arbitrary superpositions of polynomial functions and the function |x|; such sequences are referred to as polynomial-modular recursive sequences. We show how evaluations on three-tape Minsky machines can be simulated via polynomial-modular recursive sequences. Based on this result, we formulate algorithmically unsolvable problems related to polynomial-modular recursive sequences. We also consider recursive sequences in which the rules of generation are functions formed by some superpositions of polynomial functions and the function
Originally published in Diskretnaya Matematika (2022) 34, №2, 43–49 (in Russian).
Acknowledgment
The author is grateful to the referee for valuable comments and suggestions.
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Funding: Supported by the Russian Foundation for Basic Research (grant no. 19-01-00200).
References
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Articles in the same Issue
- Frontmatter
- On small distance-regular graphs with the intersection arrays {mn − 1, (m − 1)(n + 1), n − m + 1; 1, 1, (m − 1)(n + 1)}
- On algebraicity of lattices of ω-fibred formations of finite groups
- On polynomial-modular recursive sequences
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Articles in the same Issue
- Frontmatter
- On small distance-regular graphs with the intersection arrays {mn − 1, (m − 1)(n + 1), n − m + 1; 1, 1, (m − 1)(n + 1)}
- On algebraicity of lattices of ω-fibred formations of finite groups
- On polynomial-modular recursive sequences
- Classes of piecewise-quasiaffine transformations on the generalized 2-group of quaternions
- Limit theorem for a smoothed version of the spectral test for testing the equiprobability of a binary sequence
- Limit theorem for stationary distribution of a critical controlled branching process with immigration
