Translator Disclaimer
2017 Automatic sequences and curves over finite fields
Andrew Bridy
Algebra Number Theory 11(3): 685-712 (2017). DOI: 10.2140/ant.2017.11.685

Abstract

We prove that if y = n=0a(n)xn Fq[[x]] is an algebraic power series of degree d, height h, and genus g, then the sequence a is generated by an automaton with at most qh+d+g1 states, up to a vanishingly small error term. This is a significant improvement on previously known bounds. Our approach follows an idea of David Speyer to connect automata theory with algebraic geometry by representing the transitions in an automaton as twisted Cartier operators on the differentials of a curve.

Citation

Download Citation

Andrew Bridy. "Automatic sequences and curves over finite fields." Algebra Number Theory 11 (3) 685 - 712, 2017. https://doi.org/10.2140/ant.2017.11.685

Information

Received: 20 June 2016; Revised: 20 November 2016; Accepted: 19 December 2016; Published: 2017
First available in Project Euclid: 19 October 2017

zbMATH: 06722479
MathSciNet: MR3649365
Digital Object Identifier: 10.2140/ant.2017.11.685

Subjects:
Primary: 11B85
Secondary: 11G20, 14H05, 14H25

Rights: Copyright © 2017 Mathematical Sciences Publishers

JOURNAL ARTICLE
28 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.11 • No. 3 • 2017
MSP
Back to Top