A4 Refereed article in a conference publication
Geometry and Dynamics of the Besicovitch and Weyl Spaces
Authors: Ville Salo, Ilkka Törmä
Editors: Hsu-Chun Yen, Oscar H Ibarra
Publishing place: Berlin
Publication year: 2012
Journal: Lecture Notes in Computer Science
Book title : Developments in Language Theory
Series title: Lecture Notes in Computer Science
Volume: 7410
First page : 465
Last page: 470
ISBN: 978-3-642-31652-4
eISBN: 978-3-642-31653-1
ISSN: 0302-9743
DOI: https://doi.org/10.1007/978-3-642-31653-1_42
Abstract
We study the geometric properties of Cantor subshifts in the Besicovitch space, proving that sofic shifts occupy exactly the homotopy classes of simplicial complexes. In addition, we study canonical projections into subshifts, characterize the cellular automata that are contracting or isometric in the Besicovitch or Weyl spaces, study continuous functions that locally look like cellular automata, and present a new proof for the nonexistence of transitive cellular automata in the Besicovitch space.
We study the geometric properties of Cantor subshifts in the Besicovitch space, proving that sofic shifts occupy exactly the homotopy classes of simplicial complexes. In addition, we study canonical projections into subshifts, characterize the cellular automata that are contracting or isometric in the Besicovitch or Weyl spaces, study continuous functions that locally look like cellular automata, and present a new proof for the nonexistence of transitive cellular automata in the Besicovitch space.
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