Narrow Results

We prove that if π is a recursive set of primes, then pointlike sets are decidable for the pseudovariety of semigroups whose subgroups are π-groups. In particular, when π is the empty set, we obtain Henckell's decidability of aperiodic pointlikes. Our proof, restricted to the case of aperiodic semigroups, is simpler than the original proof.

Rauzy graphs of subshifts are endowed with an automaton structure. For Sturmian subshifts, it is shown that its transition semigroup is the syntactic semigroup of the language recognized by the automaton. An inverse limit of the partial semigroups of nonzero regular elements of their transition semigroups is described. If the subshift is minimal, then this inverse limit is isomorphic, as a partial semigroup, to the -class associated to it in the free pro-aperiodic semigroup.