Comparison-free polyregular functions
Year: 2021
Type: preprint
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.
Authors: Nguyên, Lê Thành Dũng Tito, Noûs, Camille, Pradic, Cécilia
Institution: University of Oxford
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W3136542949