Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T06:36:07.462Z Has data issue: false hasContentIssue false
  • English
  • Français

Drunken man infinite words complexity

Published online by Cambridge University Press:  03 June 2008

Marion Le Gonidec
Marion Le Gonidec*
Affiliation:
Institut de Mathématiques, Université de Liège, Grande traverse 12 B.37, 4000 Liège, Belgium; [email protected]
Get access

Abstract

In this article, we study the complexity of drunken man infinite words. We show that these infinite words, generated by a deterministic and complete countable automaton, or equivalently generated by a substitution over a countable alphabet of constant length, have complexity functions equivalent to n(log2n)2 when n goes to infinity.


Keywords

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 42 , Issue 3: JM'06 , July 2008 , pp. 599 - 613
Copyright
© EDP Sciences, 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allouche, J.-P., Sur la complexité des suites infinies. Bull. Belg. Math. Soc. Simon Stevin 1 (1994) 133–143.
J.-P. Allouche and J. Shallit, Automatic sequences. Theory, applications, generalizations. Cambridge University Press (2003).
J. Cassaigne, Special factors of sequences with linear subword complexity. In Developments in language theory (Magdeburg, 1995), World Sci. Publishing (1996) 25–34.
Cassaigne, J., Complexité et facteurs spéciaux. Bull. Belg. Math. Soc. Simon Stevin 4 (1997) 67–88.
Cobham, A., Uniform-tag sequences. Math. Syst. Theory 6 (1972) 164–192. CrossRef
Ferenczi, S., Complexity of sequences and dynamical systems. Discrete Math. 206 (1999) 145–154. CrossRef
Ferenczi, S., Substitution dynamical systems on infinite alphabets. Ann. Inst. Fourier 56 (2006) 2315–2343. CrossRef
Fouvry, E. and Mauduit, C., Sur les entiers dont la somme des chiffres est moyenne. J. Number Theory 114 (2005) 135–152. CrossRef
P. Kůrka, Topological and symbolic dynamics, Cours spécialisés Vol. 11, SMF (2003).
Le Gonidec, M., Sur la complexité de mots infinis engendrés par des q-automates dénombrables. Ann. Inst. Fourier 56 (2006) 2463–2491. CrossRef
M. Le Gonidec, Sur la complexité des mots q∞ -automatiques. Ph.D. thesis, Université Aix-Marseille II (2006).
Mauduit, C., Propriétés arithmétiques des substitutions et automates infinis. Ann. Inst. Fourier 56 (2006) 2525–2549. CrossRef
Mauduit, C. and Sárközy, A., On the arithmetic structure of sets characterized by sum of digits properties. J. Number Theory 61 (1996) 25–38. CrossRef
Pansiot, J.-J., Complexité des facteurs des mots infinis engendrés par morphismes itérés. Lecture Notes Comput. Sci. 172 (1985) 380–389. Automata, languages and programming (Antwerp, 1984). CrossRef
L. Staiger, Kolmogorov complexity of infinite words. CDMTCS Research Report Series 279 (2006).