The chain relation in sofic subshifts

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/approximate to that offers insight into some properties of the original subshift. Using G/approximate to 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 (straight-forward) algorithms deciding chain-transitivity and chain-mixing properties of a sofic subshift and listing all the attractors of the subshift system.