Uniformisation of two-way transducers

Abstract

We show that every relation realised by a nondeterministic two-way transducer contains a function with equal domain which can be realised by a sequential two-way transducer. Our proof is built on three structural constructions with automata: a variant of Shepherdson's method to convert a two-way automaton into an equivalent one-way automaton, which we call the folding of a two-way automaton; the construction of an unambiguous automaton for a rational language based on covering of automata; a simulation of an unambiguous automaton by a deterministic two-way one due to Hopcroft and Ullman. It follows a new proof for the fact (due to Engelfriet and Hoogeboom) that every functional two-way transducer can be converted into a sequential one, together with a clear estimation for the underlying complexity. © 2013 Springer-Verlag Berlin Heidelberg.