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Reversible Pebble Transducers

Authors Luc Dartois , Paul Gastin , Loïc Germerie Guizouarn , Shankaranarayanan Krishna

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Subject Classification

ACM Subject Classification
  • Theory of computation → Transducers
Keywords
  • Transducers
  • Polyregular functions
  • Reversibility
  • Composition
  • Uniformization

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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. [Luc Dartois et al., 2017] 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.

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Luc Dartois, Paul Gastin, Loïc Germerie Guizouarn, and Shankaranarayanan Krishna. Reversible Pebble Transducers. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 14:1-14:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CONCUR.2025.14

Author Details

Luc Dartois
  • Université Paris Est Creteil, LACL, F-94010 Créteil, France
Paul Gastin
  • Université Paris-Saclay, ENS Paris-Saclay, CNRS, LMF, 91190, Gif-sur-Yvette, France
  • CNRS, ReLaX, IRL 2000, Siruseri, India
Loïc Germerie Guizouarn
  • Univ Rennes, CNRS, Inria, IRISA - UMR 6074, F-35000 Rennes, France
Shankaranarayanan Krishna
  • Indian Institute of Technology Bombay, Mumbai, India

References

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