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Comparison-Free Polyregular Functions

Authors Lê Thành Dũng (Tito) Nguyễn , Camille Noûs, Pierre Pradic



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Lê Thành Dũng (Tito) Nguyễn
  • Laboratoire d'informatique de Paris Nord, Villetaneuse, France
Camille Noûs
  • Laboratoire Cogitamus, Université Volante, Sevran, France
Pierre Pradic
  • Department of Computer Science, University of Oxford, UK

Acknowledgements

Thanks to Mikołaj Bojańczyk and Sandra Kiefer for inspiring discussions, to Gaëtan Douéneau-Tabot and Amina Doumane for explaining some features of their work to us, to Charles Paperman for his help with bibliography and to the reviewers for their feedback.

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Lê Thành Dũng (Tito) Nguyễn, Camille Noûs, and Pierre Pradic. Comparison-Free Polyregular Functions. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 139:1-139:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.ICALP.2021.139

Abstract

This paper introduces a new automata-theoretic class of string-to-string functions with polynomial growth. Several equivalent definitions are provided: a machine model which is a restricted variant of pebble transducers, and a few inductive definitions that close the class of regular functions under certain operations. Our motivation for studying this class comes from another characterization, which we merely mention here but prove elsewhere, based on a λ-calculus with a linear type system. As their name suggests, these comparison-free polyregular functions form a subclass of polyregular functions; we prove that the inclusion is strict. We also show that they are incomparable with HDT0L transductions, closed under usual function composition - but not under a certain "map" combinator - and satisfy a comparison-free version of the pebble minimization theorem. On the broader topic of polynomial growth transductions, we also consider the recently introduced layered streaming string transducers (SSTs), or equivalently k-marble transducers. We prove that a function can be obtained by composing such transducers together if and only if it is polyregular, and that k-layered SSTs (or k-marble transducers) are closed under "map" and equivalent to a corresponding notion of (k+1)-layered HDT0L systems.

Subject Classification

ACM Subject Classification
  • Theory of computation → Transducers
Keywords
  • pebble transducers
  • HDT0L systems
  • polyregular functions

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