The Equivalence Problem for Single-Valued Two-Way Transducers (on NPDTOL Languages) is Decidable

Abstract

The equivalence problem for deterministic two-way transducers was a longstanding problem finally shown decidable by E. M. Gurari. We show a generalization of this result, namely that it is decidable whether two single-valued two-way transducers are equivalent on an NPDTOL language. We obtain this result by showing that it is even decidable whether a two-way transducer is single-valued on an NPDTOL language. Our solution is based on the compactness property of the systems of equations over a finitely generated free monoid shown recently by J. Lawrence and M. Albert and also V. S. Guba. This was a longstanding open problem known as the Ehrenfeucht Conjecture. Our approach also shows that for one-way transducers their single-valuedness on a given HDTOL language can be tested, and thus the equivalence of two single-valued one-way transducers on an HDTOL language is decidable, too.Our results imply the decidability of the HDOL and HDTOL sequence equivalence problems, also longstanding open problems solved rece...