Magic Numbers in Periodic Sequences

Automatic sequences; Constant-recursive sequences; Magic numbers; Periodic sequences; Regular sequences; Constant-recursive sequence; Deterministic finite automata; Formal languages and automata; Integer-N; Nondeterministic finite automaton; Periodic sequence; Recursive sequences; Regular sequence; Theoretical Computer Science; Computer Science (all)

Abstract :

In formal languages and automata theory, the magic number problem can be formulated as follows: for a given integer n, is it possible to find a number d in the range [ n, 2 n] such that there is no minimal deterministic finite automaton with d states that can be simulated by a minimal nondeterministic finite automaton with exactly n states? If such a number d exists, it is called magic. In this paper, we consider the magic number problem in the framework of deterministic automata with output, which are known to characterize automatic sequences. More precisely, we investigate magic numbers for periodic sequences viewed as either automatic, regular, or constant-recursive.

Disciplines :

Mathematics

Author, co-author :

Kreczman, Savinien ; Université de Liège - ULiège > Mathematics

Prigioniero, Luca ; Dipartimento di Informatica, Università degli Studi di Milano, Milan, Italy

Rowland, Eric ; Department of Mathematics, Hofstra University, Hempstead, United States

Stipulanti, Manon ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes

Language :

English

Title :

Magic Numbers in Periodic Sequences

Publication date :

2023

Event name :

14th International Conference on WORDS 2023

Event place :

Umeå, Swe

Event date :

12-06-2023 => 16-06-2023

Audience :

International

Main work title :

Combinatorics on Words - 14th International Conference, WORDS 2023, Proceedings

Editor :

Frid, Anna

Publisher :

Springer Science and Business Media Deutschland GmbH

ISBN/EAN :

978-3-03-133179-4

Pages :

206—219

Peer reviewed :

Peer reviewed

Additional URL :

https://link.springer.com/content/pdf/10.1007/978-3-031-33180-0_16

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]

Available on ORBi :

since 30 May 2024

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