2014/03/20 by Victor Marsault, Marsault, Victor, Jacques Sakarovitch +1
Biochemistry, Genetics and Molecular Biology · Computer Science · #Algorithms and Data Compression #Chemical Synthesis and Analysis #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #cs.FL #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1403.5190
21 pages, early version
openalex publication_date 2014/03/20 · arxiv created 2014/05/05 · arxiv updated 2014/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work builds on the notion of breadth-first signature of infinite trees and (prefix-closed) languages introduced by the authors in a previous work. We focus here on periodic signatures, a case coming from the study of rational base numeration systems; the language of integer representations in base~(p)/(q) has a purely periodic signature whose period is derived from the Christoffel word of slope~(p)/(q). Conversely, we characterise languages whose signature are purely periodic as representations of integers in such number systems with non-canonical alphabets of digits.