Constructing Sequential Bijections

. We state a simple condition on a rational subset X of a free monoid B for the existence of a sequential function that is a one-to-one mapping of some free monoid A onto X. As a by-product we obtain new sequential bijections of a free monoid onto another. 1 Introduction The starting point of the present paper is a simple question. Given two free monoids A (the "input" monoid) and B (the "output" monoid) respectively generated by m and n elements, design an effective function that is as elementary as possible and that maps bijectively A onto B . A natural solution uses the free monoid over m (resp. n) letters as a representation set of the integers in base m (resp. n); the problem of the leading zeros can be solved by resorting to the so-called p-adic representation instead of the standard one. But actually we use a less elaborate computation model. Provide each transition of a finite deterministic automaton on A with an element in the free monoid B . The dete..