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### Abstract

Regular rewriting rules play a significant role in text-processing
techniques. It is well known that they can be expressed in terms of
rational functions and consequently for each such rule one can
efficiently construct a transducer or,
equivalently a bimachine. Unfortunately the transducers, in general,
cannot be determinized and the bimachines do not allow to stream a
text, and thus one cannot process a text on-line.
We propose a new formalism, which aims at preserving the determinism
and still to be able to process the input sequentially, i.e. whithout
disposing on the entire text in advance. To this end we incorporate an
additional infinite memory,
represented as FIFO. We model it in a way to garantee the desired
properties and to assure linear traversal of an input text.
We call these machines \textit{FIFO-transducers} and study their
properties with respect to rational functions. Our main efforts
concern the composition problem. We shall that we can efficiently
compose FIFO-transducers with subsequentional transducers, but in
general they are not closed under composition and they are unable to
describe the class of all rational function. We also show a simple
example of function that is not rational but can be represented by
such a machine.
Finally, we define a subclass of rational functions that can be
recognized by FIFO-transducers but (in the general case) not by a
subsequenbtial transducer. We state sufficient conditions for a
regular rule in order to be represented by a FIFO-transducer and show
how to check these properties algorithmically.