Generalised Twinning Property

Stefan Gerdjikov

Abstract: In this paper we consider the problem of sequentialisation of rational functions \(f:\varSigma ^*\rightarrow \mathcal{M}\). We introduce a class of monoids that includes infinitary groups, free monoids, tropical monoids and is closed under Cartesian Product. For this class of monoids we provide a sequentialisation construction for transducers and appropriately generalise the notion of Twinning Property. We provide a construction to test the Twinning Property for transducers over the considered class of monoids and prove that it is a necessary and sufficient condition for the sequentialisation construction to terminate.