State Complexity of Testing Divisibility

State Complexity of Testing Divisibility

Under some mild assumptions, we study the state complexity of the trim minimal automaton accepting the greedy representations of the multiples of m >= 2 for a wide class of linear numeration systems. As an example, the number of states of the trim minimal automaton accepting the greedy repres...

Full description

Bibliographic Details
Main Authors: Emilie Charlier, Narad Rampersad, Michel Rigo, Laurent Waxweiler
Format: Article
Language:English
Published: Open Publishing Association 2010-08-01
Series:Electronic Proceedings in Theoretical Computer Science
Online Access:http://arxiv.org/pdf/1008.1668v1
id doaj-35971ca60e5e454482f95f746e1453b8
record_format Article
spelling doaj-35971ca60e5e454482f95f746e1453b82020-11-24T21:48:56ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802010-08-0131Proc. DCFS 2010485710.4204/EPTCS.31.7State Complexity of Testing DivisibilityEmilie CharlierNarad RampersadMichel RigoLaurent WaxweilerUnder some mild assumptions, we study the state complexity of the trim minimal automaton accepting the greedy representations of the multiples of m >= 2 for a wide class of linear numeration systems. As an example, the number of states of the trim minimal automaton accepting the greedy representations of the multiples of m in the Fibonacci system is exactly 2m^2. http://arxiv.org/pdf/1008.1668v1
collection DOAJ
language English
format Article
sources DOAJ
author Emilie Charlier
Narad Rampersad
Michel Rigo
Laurent Waxweiler
spellingShingle Emilie Charlier
Narad Rampersad
Michel Rigo
Laurent Waxweiler
State Complexity of Testing Divisibility
Electronic Proceedings in Theoretical Computer Science
author_facet Emilie Charlier
Narad Rampersad
Michel Rigo
Laurent Waxweiler
author_sort Emilie Charlier
title State Complexity of Testing Divisibility
title_short State Complexity of Testing Divisibility
title_full State Complexity of Testing Divisibility
title_fullStr State Complexity of Testing Divisibility
title_full_unstemmed State Complexity of Testing Divisibility
title_sort state complexity of testing divisibility
publisher Open Publishing Association
series Electronic Proceedings in Theoretical Computer Science
issn 2075-2180
publishDate 2010-08-01
description Under some mild assumptions, we study the state complexity of the trim minimal automaton accepting the greedy representations of the multiples of m >= 2 for a wide class of linear numeration systems. As an example, the number of states of the trim minimal automaton accepting the greedy representations of the multiples of m in the Fibonacci system is exactly 2m^2.
url http://arxiv.org/pdf/1008.1668v1
work_keys_str_mv AT emiliecharlier statecomplexityoftestingdivisibility
AT naradrampersad statecomplexityoftestingdivisibility
AT michelrigo statecomplexityoftestingdivisibility
AT laurentwaxweiler statecomplexityoftestingdivisibility
_version_ 1725890439678001152

Similar Items