Reversible Pebble Transducers

TL;DR

This paper introduces reversible pebble transducers to improve the efficiency of composing complex string-to-string functions, reducing the exponential blow-up associated with traditional methods.

Contribution

It presents the first efficient uniformization and composition techniques for reversible pebble transducers, addressing complexity issues in previous approaches.

Findings

Efficient uniformization of non-deterministic pebble transducers to reversible ones

Polynomial complexity in composing reversible pebble transducers

Reduction of exponential blow-up in transducer composition

Abstract

Deterministic two-way transducers with pebbles (aka pebble transducers) capture the class of polyregular functions, which extend the string-to-string regular functions allowing polynomial growth instead of linear growth. One of the most fundamental operations on functions is composition, and (poly)regular functions can be realized as a composition of several simpler functions. In general, composition of deterministic two-way transducers incur a doubly exponential blow-up in the size of the inputs. A major improvement in this direction comes from the fundamental result of Dartois et al. [10] showing a polynomial construction for the composition of reversible two-way transducers. A precise complexity analysis for existing composition techniques of pebble transducers is missing. But they rely on the classic composition of two-way transducers and inherit the double exponential complexity. To overcome this problem, we introduce reversible pebble transducers. Our main results are efficient uniformization techniques for non-deterministic pebble transducers to reversible ones and efficient composition for reversible pebble transducers.