REFLEXIVE RELATIONS, EXTENSIVE TRANSFORMATIONS AND PIECEWISE TESTABLE LANGUAGES OF A GIVEN HEIGHT
Mikhail Vladimirovich Volkov · International Journal of Algebra and Computation · 2004
Straubing deduced from Simon's theorem that monoids of reflexive relations as well as monoids of order preserving extensive transformations generate the pseudovariety of [Formula: see text]-trivial monoids. We refine these results by showing that each pseudovariety in Simon's hierarchy of [Formula: see text]-trivial monoids is generated by a single relation/transformation monoid. From this and from some results by Blanchet–Sadri we obtain a complete solution of the finite basis problem for Straubing's monoids.