Computability by finite automata and pisot bases

Daniel Berend; Christiane Frougny

doi:10.1007/BF01578846

Computability by finite automata and pisot bases

Daniel Berend, Christiane Frougny

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

We prove that the function of normalization in base θ, which maps any θ-representation of a real number onto its θ-development, obtained by a greedy algorithm, is a function computable by a finite automaton over any alphabet if and only if θ is a Pisot number.

Original language	English
Pages (from-to)	275-282
Number of pages	8
Journal	Mathematical Systems Theory
Volume	27
Issue number	3
DOIs	https://doi.org/10.1007/BF01578846
State	Published - 1 May 1994

ASJC Scopus subject areas

Theoretical Computer Science
General Mathematics
Computational Theory and Mathematics

Access to Document

10.1007/BF01578846

Cite this

@article{3e3e463ba3894d0bbfa075734fada54d,

title = "Computability by finite automata and pisot bases",

abstract = "We prove that the function of normalization in base θ, which maps any θ-representation of a real number onto its θ-development, obtained by a greedy algorithm, is a function computable by a finite automaton over any alphabet if and only if θ is a Pisot number.",

author = "Daniel Berend and Christiane Frougny",

year = "1994",

month = may,

day = "1",

doi = "10.1007/BF01578846",

language = "English",

volume = "27",

pages = "275--282",

journal = "Mathematical Systems Theory",

issn = "0025-5661",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - Computability by finite automata and pisot bases

AU - Berend, Daniel

AU - Frougny, Christiane

PY - 1994/5/1

Y1 - 1994/5/1

N2 - We prove that the function of normalization in base θ, which maps any θ-representation of a real number onto its θ-development, obtained by a greedy algorithm, is a function computable by a finite automaton over any alphabet if and only if θ is a Pisot number.

AB - We prove that the function of normalization in base θ, which maps any θ-representation of a real number onto its θ-development, obtained by a greedy algorithm, is a function computable by a finite automaton over any alphabet if and only if θ is a Pisot number.

UR - http://www.scopus.com/inward/record.url?scp=0001510584&partnerID=8YFLogxK

U2 - 10.1007/BF01578846

DO - 10.1007/BF01578846

M3 - Article

AN - SCOPUS:0001510584

SN - 0025-5661

VL - 27

SP - 275

EP - 282

JO - Mathematical Systems Theory

JF - Mathematical Systems Theory

IS - 3

ER -

Computability by finite automata and pisot bases

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this