Ultimate periodicity problem for linear numeration systems

Charlier, Emilie; Massuir, Adeline; Rigo, Michel; Rowland, E.

doi:10.1142/S0218196722500254

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Ultimate periodicity problem for linear numeration systems

Charlier, Emilie; Massuir, Adeline; Rigo, Michel et al.

2022 • In International Journal of Algebra and Computation, 32, p. 561-596

Peer Reviewed verified by ORBi

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https://hdl.handle.net/2268/290293

DOI
10.1142/S0218196722500254

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Keywords :

automata theory; Decision problem; linear recurrent sequence; numeration system; p-adic valuation; Mathematics (all); General Mathematics

Abstract :

[en] We address the following decision problem. Given a numeration system U and a U-recognizable subset X of N, i.e. the set of its greedy U-representations is recognized by a finite automaton, decide whether or not X is ultimately periodic. We prove that this problem is decidable for a large class of numeration systems built on linear recurrence sequences. Based on arithmetical considerations about the recurrence equation and on p-adic methods, the DFA given as input provides a bound on the admissible periods to test.

Disciplines :

Mathematics

Author, co-author :

Charlier, Emilie ; Université de Liège - ULiège > Mathematics

Massuir, Adeline ; Université de Liège - ULiège > Mathematics

Rigo, Michel ; Université de Liège - ULiège > Département de mathématique

Rowland, E.; Department of Mathematics, Hofstra University, Hempstead, United States

Language :

English

Title :

Ultimate periodicity problem for linear numeration systems

Publication date :

2022

Journal title :

International Journal of Algebra and Computation

ISSN :

0218-1967

Publisher :

World Scientific

Volume :

Pages :

561-596

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://www.worldscientific.com/doi/pdf/10.1142/S0218196722500254

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since 05 May 2022

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