Semigroups and languages of dot-depth two
The author discusses the problem of membership of a finite monoid M in the i-th member \({\mathcal V}_ i\) of a sequence of pseudo-varieties of monoids corresponding to the varieties of regular languages forming the so called Brzozowski hierarchy of locally testable languages. He gives two partial results: a necessary condition for M to belong to \({\mathcal V}_ 2\); for a 2-generated M it is also a sufficient condition.
scientific article; zbMATH DE number 4069152
scientific article