A General Class of Monoids Supporting Canonisation and Minimisation of (Sub)sequential Transducers

Stefan Gerdjikov

Abstract: In this paper we consider the problems of canonisation and minimisation of subsequential transducer with output in an arbitrary monoid. We show that these problems can be efficiently solved for a large class of monoids that includes the free monoids, tropical monoid, and groups, and is closed under Cartesian Product. We describe this class of monoids in terms of five simple axioms. The first four of them seem to be natural. For the last one, we show that it is also necessary.