2018/01/15 by Gool, Samuel J. v., Steinberg, B.
#20M07 #20M35 #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1801.04638
For a variety of finite groups \mathbf H, let \mathbf H denote the variety of finite semigroups all of whose subgroups lie in \mathbf H. We give a characterization of the subsets of a finite semigroup that are pointlike with respect to \mathbf H. Our characterization is effective whenever \mathbf H has a decidable membership problem. In particular, the separation problem for \mathbf H-languages is decidable for any decidable variety of finite groups \mathbf H. This generalizes Henckell's theorem on decidability of aperiodic pointlikes.