The chain relation in sofic subshifts

Details The chain relation in sofic subshifts The chain relation in sofic subshifts

2009-11-29

arxiv.org/abs/0911.5475v1

Fundamenta Informaticae. volume 84. number 3-4. pages 375-390. 2008

Mathematics

Dynamical Systems

14 pages, 9 figures, preprint (final version published in Fundamenta Informaticae)

Scientific paper

The paper gives a characterisation of the chain relation of a sofic subshift. Every sofic subshift $\Sigma$ can be described by a labelled graph $G$. Factorising $G$ in a suitable way we obtain the graph $G/_\approx$ that offers insight into some properties of the original subshift. Using $G/_\approx$ we describe first the chain relation in $\Sigma$, then characterise chain-transitive sofic subshifts, chain-mixing sofic subshifts and finally the attractors of the subshift dynamic system. At the end we present (straightforward) algorithms deciding chain-transitivity and chain-mixing properties of a sofic subshift and listing all the attractors of the subshift system.

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