An efficient algorithm to decide periodicity of b-recognisable sets using MSDF convention

[en] Given an integer base b>1, a set of integers is represented in base b by a language over {0,1,...,b-1}. The set is said to be b-recognisable if its representation is a regular language. It is known that eventually periodic sets are b-recognisable in every base b, and Cobham's theorem implies the converse: no other set is b-recognisable in every base b. We are interested in deciding whether a $b$-recognisable set of integers (given as a finite automaton) is eventually periodic. Honkala showed that this problem is decidable in 1986 and recent developments give efficient decision algorithms. However, they only work when the integers are written with the least significant digit first. In this work, we consider the natural order of digits (Most Significant Digit First) and give a quasi-linear algorithm to solve the problem in this case.

Research Center/Unit :

Mathématiques
Montefiore Institute - Montefiore Institute of Electrical Engineering and Computer Science - ULiège

Disciplines :

Mathematics
Computer science

Author, co-author :

Boigelot, Bernard ; Université de Liège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Informatique

Mainz, Isabelle ; Université de Liège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Dép. d'électric., électron. et informat. (Inst.Montefiore)

Marsault, Victor ; Université de Liège > Département de mathématique > Mathématiques discrètes

Rigo, Michel ; Université de Liège > Département de mathématique > Mathématiques discrètes

Language :

English

Title :

An efficient algorithm to decide periodicity of b-recognisable sets using MSDF convention

Publication date :

August 2017

Event name :

The 44th International Colloquium on Automata, Languages, and Programming

Event organizer :

University of Warsaw

Event place :

Warsaw, Poland

Event date :

Du 10 juillet 2017 au 14 juillet 2017

Audience :

International

Journal title :

Leibniz International Proceedings in Informatics

ISSN :

1868-8969

Publisher :

Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Germany

Volume :

Peer reviewed :

Peer Reviewed verified by ORBi

Funders :

European Union. Marie Skłodowska-Curie Actions

Commentary :

Long version at : https://arxiv.org/abs/1702.03715

Available on ORBi :

since 23 June 2017

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Bibliography

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