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The Chain Relation in Sofic Subshifts

Kazda A.

Fundamenta Informaticae

2008

Vol. 84, nr 3-4

375-390

The paper gives a characterisation of the chain relation of a sofic subshift. Every sofic subshift S can be described by a labelled graph G. Factorising G in a suitable way we obtain the graph G/ ť that offers insight into some properties of the original subshift. Using G/ ť 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.