A graph approach to computing nondeterminacy in substitutional
dynamical systems
A graph approach to computing nondeterminacy in substitutional
dynamical systems
- Author: Toke M. Carlsen and Søren Eilers.
- Date: December 2002, revised version February 2002.
- Status: Submitted.
- Pages: 24.
- Abstract: Determining $K-groups of certain C*-algebras we found
an invariant of flow equivalence --- akin and related to the dimension
groups considered in work of Durand, Host and Skau --- of substitutional systems based on
combinatorial and textual properties of the special elements. To
investigate the invariant, we were
naturally lead to concern ourselves with computability of certain
words and quantities associated to the class of special elements
associated to a given substitution, and failing to find algorithms
meeting our needs in the literature, we developed the approach
presented in the present note. Our algorithm outputs a finite representation of
each special word, and determines when such
representations are equivalent under tail equivalence, a
naturally occurring relation of importance in our invariant.
- Remarks:
- Program implementing the algorithm:
- Access opportunities:
eilers@math.ku.dk/March
2003.