Pointlike sets with respect to ER

TL;DR

This paper proves that pointlike sets are decidable for a specific class of finite semigroups and provides a constructive method to compute ER-pointlike subsets using relational morphisms.

Contribution

It introduces a decidability result for pointlike sets in a new class of finite semigroups and offers an explicit computational approach.

Findings

Decidability of pointlike sets for semigroups with R-trivial idempotent-generated subsemigroup

Construction of an explicit relational morphism for computing ER-pointlike subsets

Provides a constructive proof with practical computational implications

Abstract

We show that pointlike sets are decidable for the pseudovariety of finite semigroups whose idempotent-generated subsemigroup is R-trivial. Notably, our proof is constructive: we provide an explicit relational morphism which computes the ER-pointlike subsets of a given finite semigroup.