Abstract
Hamachi and Inoue obtained a necessary and sufficient condition for the embeddability of an irreducible subshift of finite type into a Dyck shift (Embedding of shifts of finite type into the Dyck shift, Monatsh. Math. 145 (2005), 107–129). Krieger introduced a property A of subshifts that is an invariant of topological conjugacy and he constructed for property A subshifts an invariantly associated semigroup (with zero) (On a syntactically defined invariant of symbolic dyanamics, Ergod. Th. Dynam. Sys. 20 (2000), 501–516). We introduce a class of property A subshifts, of which the Dyck shifts are prototypes, to which there are associated inverse semigroups (with zero) that arise from finite directed graphs. These subshifts also allow a suitable presentation by a finite directed graph that is labeled by elements of the associated inverse semigroup. We extend the criterion for embeddability of an irreducible subshift of finite type from the Dyck shifts to target shifts in this class.
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