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UID:5827@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20221213T110000
DTEND;TZID=Europe/Paris:20221213T120000
DTSTAMP:20241120T200228Z
URL:https://www.i2m.univ-amu.fr/evenements/a-annoncer-3/
SUMMARY:Pierre Béaur (Univ. Paris-Saclay): Walking On A Line: finding S-ad
 ic walks in an ω-automaton
DESCRIPTION:Pierre Béaur: At the heart of symbolic dynamics lies the study
  of languages\, infinite words and the dynamical structures associated. We
  focus on two classical methods to generate such structures. The first one
  relies on substitutions\, which are morphisms on words\, by iterating one
  on an initial letter\, and considering the limit word. This substitutive 
 approach was generalized by allowing the use of multiple substitutions\, t
 hus leading to the notion of S-adic representations. The second method to 
 generate symbolic structures is to consider the infinite walks on a labele
 d graph (or ω-automaton).\n\nIn this presentation\, I consider decidabili
 ty questions at the crossing between these two points of view. Given an ω
 -automaton A\, and a substitution σ\, does A accept the infinite substitu
 tive words generated by σ? The main result of this presentation is that\,
  using elementary notions of formal languages\, we can build a new tool to
  decide such questions. In the S-adic framework\, this tool also solves si
 milar questions: given an ω-automaton A\, does A accept a Sturmian word? 
 an Arnoux-Rauzy word? We also use this tool to derive results on the struc
 ture of S-adic representations allowed in an ω-automaton\, on the structu
 re of ω-automata accepting substitutive words\, and on the combinatorics 
 of Sturmian words.
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 022/12/Pierre_Beaur.png
CATEGORIES:Séminaire,Ernest
LOCATION:I2M Luminy - Ancienne BU\, Salle Séminaire2 (RdC)\, 163 Avenue de
  Luminy\, 13009 Marseille\, France\, 
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, 1300
 9 Marseille\, France\, ;X-APPLE-RADIUS=100;X-TITLE=I2M Luminy - Ancienne B
 U\, Salle Séminaire2 (RdC):geo:0,0
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