On the composition of morphisms and inverse morphisms

Compositional representation of rational functions

“…We start with a general result which connects these compositions to the general morphic compositions for which a hierarchy was given in [7]. I H, because the latter class consists of functions only.…”

“…We adapt now the general idea (see [7] or [10]) behind the construction of equivalent rational compositions for transducers in order to obtain an 'injective' representation for rational functions.…”

“…Here m is an endmarker symbol and σ is a composition of morphisms and inverse morphisms. The endmarker can in general not be avoided, see [7] and [4]. The transductions realized by simple transducers can, however, be represented without the use of endmarkers.…”

“…The transductions realized by simple transducers can, however, be represented without the use of endmarkers. In [10] and in [7] it has been shown that they form precisely the class of mappings representable by a composition of morphisms and inverse morphisms. In addition it is known from [7] and [8] that such compositions can be assumed to be of length four.…”

“…In [10] and in [7] it has been shown that they form precisely the class of mappings representable by a composition of morphisms and inverse morphisms. In addition it is known from [7] and [8] that such compositions can be assumed to be of length four. As a matter of fact length four is necessary and sufficient to characterize the whole class of these compositions.…”