The purpose of this paper is to show connections between iterated
length-preserving rational transductions and linear space
computations. Hence, we study the smallest family of transductions
containing length-preserving rational transductions and closed under
union, composition and iteration. We give several characterizations of
this class using restricted classes of length-preserving rational
transductions, by showing the connections with "context-sensitive
transductions" and transductions associated with recognizable picture
languages.