A graph approach to computing nondeterminacy in substitutional dynamical systems

Toke M. Carlsen; Søren Eilers

RAIRO - Theoretical Informatics and Applications (2007)

  • Volume: 41, Issue: 3, page 285-306
  • ISSN: 0988-3754

Abstract

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We present an algorithm which for any aperiodic and primitive substitution outputs a finite representation of each special word in the shift space associated to that substitution, and determines when such representations are equivalent under orbit and shift tail equivalence. The algorithm has been implemented and applied in the study of certain new invariants for flow equivalence of substitutional dynamical systems.

How to cite

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Carlsen, Toke M., and Eilers, Søren. "A graph approach to computing nondeterminacy in substitutional dynamical systems ." RAIRO - Theoretical Informatics and Applications 41.3 (2007): 285-306. <http://eudml.org/doc/250063>.

@article{Carlsen2007,
abstract = { We present an algorithm which for any aperiodic and primitive substitution outputs a finite representation of each special word in the shift space associated to that substitution, and determines when such representations are equivalent under orbit and shift tail equivalence. The algorithm has been implemented and applied in the study of certain new invariants for flow equivalence of substitutional dynamical systems. },
author = {Carlsen, Toke M., Eilers, Søren},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Sustitution; shift spaces; special elements; orbit equivalence; shift tail equivalence; sustitution},
language = {eng},
month = {9},
number = {3},
pages = {285-306},
publisher = {EDP Sciences},
title = {A graph approach to computing nondeterminacy in substitutional dynamical systems },
url = {http://eudml.org/doc/250063},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Carlsen, Toke M.
AU - Eilers, Søren
TI - A graph approach to computing nondeterminacy in substitutional dynamical systems
JO - RAIRO - Theoretical Informatics and Applications
DA - 2007/9//
PB - EDP Sciences
VL - 41
IS - 3
SP - 285
EP - 306
AB - We present an algorithm which for any aperiodic and primitive substitution outputs a finite representation of each special word in the shift space associated to that substitution, and determines when such representations are equivalent under orbit and shift tail equivalence. The algorithm has been implemented and applied in the study of certain new invariants for flow equivalence of substitutional dynamical systems.
LA - eng
KW - Sustitution; shift spaces; special elements; orbit equivalence; shift tail equivalence; sustitution
UR - http://eudml.org/doc/250063
ER -

References

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  13. K. Matsumoto, Bowen-Franks groups as an invariant for flow equivalence of subshifts. Ergodic Theory Dynam. Systems21 (2001) 1831–1842.  Zbl1001.37009
  14. B. Mossé, Puissances de mots et reconnaissabilité des points fixes d'une substitution. Theoret. Comput. Sci.99 (1992) 327–334.  Zbl0763.68049
  15. J.-J. Pansiot, Decidability of periodicity for infinite words. RAIRO-Theor. Inf. Appl.20 (1986) 43–46.  Zbl0617.68063
  16. B. Parry and D. Sullivan, A topological invariant of flows on 1-dimensional spaces. Topology14 (1975) 297–299.  Zbl0314.54045
  17. M. Queffélec, Substitution dynamical systems—spectral analysis. Springer-Verlag, Berlin (1987).  Zbl0642.28013
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  19. H. Wielandt, Unzerlegbare, nicht negative Matrizen. Math. Z.52 (1950) 642–648.  

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