19 research outputs found
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 â but not under a certain âmapâcombinator â 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 âmapâ and equivalent to acorresponding notion of (k + 1)-layered HDT0L systems
Equivalence Problems for Tree Transducers: A Brief Survey
The decidability of equivalence for three important classes of tree
transducers is discussed. Each class can be obtained as a natural restriction
of deterministic macro tree transducers (MTTs): (1) no context parameters,
i.e., top-down tree transducers, (2) linear size increase, i.e., MSO definable
tree transducers, and (3) monadic input and output ranked alphabets. For the
full class of MTTs, decidability of equivalence remains a long-standing open
problem.Comment: In Proceedings AFL 2014, arXiv:1405.527
Easy cases of the D0L sequence equivalence problem
AbstractTo test the equivalence of two binary D0L sequences it suffices to compare the first four terms of the sequences. We introduce a larger class of D0L systems for which sequence equivalence can be decided by considering the first ten initial terms