Characterisation of (Sub)sequential Rational Functions over a General Class Monoids

This work provides a theoretical framework for formal language theory, but it appears incremental as it extends known characterizations to a broader class of monoids.

The authors tackled the problem of characterizing (sub)sequential rational functions over a general class of monoids by establishing a congruence relation similar to the Myhill-Nerode relation, and they identified a class of monoids defined by algebraic axioms that includes free monoids, groups, and the tropical monoid, and is closed under Cartesian products.