Comparison-Free Polyregular Functions.

This paper introduces a new automata-theoretic class of string-to-string functions with polynomialgrowth. Several equivalent definitions are provided: a machine model which is a restricted variant ofpebble transducers, and a few inductive definitions that close the class of regular functions undercertain 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 polyregularfunctions; we prove that the inclusion is strict. We also show that they are incomparable withHDT0L 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 introducedlayered streaming string transducers (SSTs), or equivalently k-marble transducers. We prove that afunction 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 acorresponding notion of (k + 1)-layered HDT0L systems

Equivalence of finite-valued streaming string transducers is decidable

In this paper we provide a positive answer to a question left open by Alur and and Deshmukh in 2011 by showing that equivalence of finite-valued copyless streaming string transducers is decidable

Survey : Weighted extended top-down tree transducers part I. : basics and expressive power

Weighted extended top-down tree transducers (transducteurs généralisés descendants [Arnold, Dauchet: Bi-transductions de forêts. ICALP'76. Edinburgh University Press, 1976]) received renewed interest in the field of Natural Language Processing, where they are used in syntax-based machine translation. This survey presents the foundations for a theoretical analysis of weighted extended top-down tree transducers. In particular, it discusses essentially complete semirings, which are a novel concept that can be used to lift incomparability results from the unweighted case to the weighted case even in the presence of infinite sums. In addition, several equivalent ways to define weighted extended top-down tree transducers are presented and the individual benefits of each presentation is shown on a small result