# Untwisting two-way transducers in elementary time

## TL;DR

This paper presents a new algorithm with double exponential space complexity for deciding if two-way transducers can be implemented by one-way transducers, improving the understanding of their computational properties.

## Contribution

It introduces a novel algorithm for deciding the implementability of two-way transducers by one-way transducers with elementary time complexity.

## Key findings

- Decidable whether a two-way transduction can be realized by a one-way transducer.
- Algorithm operates with double exponential space complexity.
- Applied technique to determine if transductions can be implemented by sweeping transducers.

## Abstract

Functional transductions realized by two-way transducers (equivalently, by streaming transducers and by MSO transductions) are the natural and standard notion of "regular" mappings from words to words. It was shown recently (LICS'13) that it is decidable if such a transduction can be implemented by some one-way transducer, but the given algorithm has non-elementary complexity. We provide an algorithm of different flavor solving the above question, that has double exponential space complexity. We further apply our technique to decide whether the transduction realized by a two-way transducer can be implemented by a sweeping transducer, with either known or unknown number of passes.

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Source: https://tomesphere.com/paper/1701.02502