The Join of the Varieties of R-trivial and L-trivial Monoids via Combinatorics on Words
Manfred Kufleitner, Alexander Lauser
Abstract
The join of two varieties is the smallest variety containing both. In
finite semigroup theory, the varieties of
R-trivial and
L-trivial monoids are two of the most
prominent classes of finite monoids. Their join is known to be
decidable due to a result of Almeida and Azevedo. In this paper, we
give a new proof for Almeida and Azevedo's effective characterization
of the join of R-trivial and
L-trivial monoids. This
characterization is a single identity of ω-terms
using three variables.
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