Efficient Construction of Reversible Transducers from Regular Transducer Expressions

TL;DR

This paper presents an efficient method to convert regular transducer expressions into two-way reversible transducers, enabling faster and more manageable implementations of regular transformations with improved composition properties.

Contribution

It introduces a construction for two-way reversible transducers from RTEs, with size bounds depending on the expression features, improving practical applicability.

Findings

Constructed 2RFTs are deterministic and co-deterministic, allowing linear-time evaluation.

Size of 2RFTs is doubly exponential in the worst case, exponential for simpler RTEs.

The method improves the efficiency of implementing regular transformations in algorithmic applications.

Abstract

The class of regular transformations has several equivalent characterizations such as functional MSO transductions, deterministic two-way transducers, streaming string transducers, as well as regular transducer expressions (RTE). For algorithmic applications, it is very common and useful to transform a specification, here, an RTE, to a machine, here, a transducer. In this paper, we give an efficient construction of a two-way reversible transducer (2RFT) equivalent to a given RTE. 2RFTs are a well behaved class of transducers which are deterministic and co-deterministic (hence allows evaluation in linear time \wrt the input word), and where composition has only polynomial complexity. We show that, for full RTE, the constructed 2RFT has size doubly exponential in the size of the expression, while, if the RTE does not use Hadamard product or chained-star, the constructed 2RFT has size exponential in the size of the RTE.