Article (Scientific journals)
The minimal automaton recognizing mN in a linear numeration system
Charlier, Emilie; Rampersad, Narad; Rigo, Michel et al.
2011In Integers, 11B (A4), p. 1-24
Peer Reviewed verified by ORBi
 

Files


Full Text
CRRW-final-integers.pdf
Author postprint (229.14 kB)
Download

All documents in ORBi are protected by a user license.

Send to



Details



Keywords :
Numeration System; Bertrand System; Beta-expansion; State Complexity; Parry Number; Finite Automaton
Abstract :
[en] We study the structure of automata accepting the greedy representations of N in a wide class of numeration systems. We describe the conditions under which such automata can have more than one strongly connected component and the form of any such additional components. Our characterization applies, in particular, to any automaton arising from a Bertrand numeration system. Furthermore, we show that for any automaton A arising from a system with a dominant root beta>1, there is a morphism mapping A onto the automaton arising from the Bertrand system associated with the number beta. Under some mild assumptions, we also study the state complexity of the trim minimal automaton accepting the greedy representations of the multiples of m>1 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 mN in the Fibonacci system is exactly 2m^2.
Disciplines :
Computer science
Mathematics
Author, co-author :
Charlier, Emilie  ;  Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Rampersad, Narad ;  Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Rigo, Michel  ;  Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Waxweiler, Laurent ;  Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
The minimal automaton recognizing mN in a linear numeration system
Publication date :
2011
Journal title :
Integers
eISSN :
1553-1732
Publisher :
Integers, Carrollton, United States - Georgia
Special issue title :
Proceedings of the Leiden Numeration Conference 2010
Volume :
11B
Issue :
A4
Pages :
1-24
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 20 January 2011

Statistics


Number of views
210 (43 by ULiège)
Number of downloads
104 (15 by ULiège)

Bibliography


Similar publications



Contact ORBi