Alexi Block Gorman ; Philipp Hieronymi ; Elliot Kaplan ; Ruoyu Meng ; Erik Walsberg et al. - Continuous Regular Functions

lmcs:5301 - Logical Methods in Computer Science, February 14, 2020, Volume 16, Issue 1 - https://doi.org/10.23638/LMCS-16(1:17)2020
Continuous Regular FunctionsArticle

Authors: Alexi Block Gorman ; Philipp Hieronymi ; Elliot Kaplan ; Ruoyu Meng ; Erik Walsberg ; Zihe Wang ; Ziqin Xiong ; Hongru Yang

    Following Chaudhuri, Sankaranarayanan, and Vardi, we say that a function f:[0,1][0,1] is r-regular if there is a Büchi automaton that accepts precisely the set of base rN representations of elements of the graph of f. We show that a continuous r-regular function f is locally affine away from a nowhere dense, Lebesgue null, subset of [0,1]. As a corollary we establish that every differentiable r-regular function is affine. It follows that checking whether an r-regular function is differentiable is in PSPACE. Our proofs rely crucially on connections between automata theory and metric geometry developed by Charlier, Leroy, and Rigo.


    Volume: Volume 16, Issue 1
    Published on: February 14, 2020
    Accepted on: November 26, 2019
    Submitted on: March 21, 2019
    Keywords: Computer Science - Logic in Computer Science,Mathematics - Logic

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