Pointlike sets with respect to R and J

We present an algorithm to compute the pointlike subsets of a finite semigroup with respect to the pseudovariety R of all finite RR-trivial semigroups. The algorithm is inspired by Henckell’s algorithm for computing the pointlike subsets with respect to the pseudovariety of all finite aperiodic semigroups. We also give an algorithm to compute J-pointlike sets, where J denotes the pseudovariety of all finite JJ-trivial semigroups. We finally show that, in contrast with the situation for R, the natural adaptation of Henckell’s algorithm to J computes pointlike sets, but not all of them.