RAIRO - Theoretical Informatics and Applications

Research Article

A graph approach to computing nondeterminacy in substitutional dynamical systems

Toke M. Carlsena1a2 and Søren Eilersa3

a1 University of Copenhagen, Universitetsparken 5, 2100 Copenhagen Ø, Denmark; toke@math.ku.dk

a2 School of Mathematical & Physical Sciences, Mathemathics Building - V123, University of Newcastle, University Drive, Callaghan NSW 2308, Australia.

a3 University of Copenhagen, Universitetsparken 5, 2100 Copenhagen Ø, Denmark; eilers@math.ku.dk

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.

(Received July 5 2004)

(Accepted August 1 2006)

(Online publication September 25 2007)

Key Words:

  • Sustitution;
  • shift spaces;
  • special elements;
  • orbit equivalence;
  • shift tail equivalence

Mathematics Subject Classification:

  • 37B10;
  • 68R15
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