Work

Abstract numeration systems on bounded languages and multiplication by a constant

Year: 2007

Type: preprint

Abstract: A set of integers is $S$-recognizable in an abstract numeration system $S$ if the language made up of the representations of its elements is accepted by a finite automaton. For abstract numeration systems built over bounded languages with at least three letters, we show that multiplication by an integer $λ\ge2$ does not preserve $S$-recognizability, meaning that there always exists a $S$-recognizable set $X$ such that $λX$ is not $S$-recognizable. The main tool is a bijection between the representation of an integer over a bounded language and its decomposition as a sum of binomial coefficients with certain properties, the so-called combinatorial numeration system.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.0706.0431

Authors: Charlier, Emilie, Rigo, Michel, Steiner, Wolfgang

Institutions: University of Liège, Laboratoire d'Informatique Algorithmique: Fondements et Applications

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2963282767

Cites: 9

Cited by: 10

Related to: 10