Vol. 9, No. 3, 2020

Download this article
Download this article For screen
For printing
Recent Issues
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
founded and published with the
scientific support and advice of the
Moscow Institute of
Physics and Technology
 
ISSN (electronic): 2640-7361
ISSN (print): 2220-5438
Previously Published
Author Index
To Appear
 
Other MSP Journals
On defining linear orders by automata

Bruno Courcelle, Irène Durand and Michael Raskin

Vol. 9 (2020), No. 3, 253–291
Abstract

Motivated by enumeration problems, we define linear orders Z on Cartesian products Z := X1×X2××Xn and on subsets of X1 × X2 where each component set Xi is [0,p] or , ordered in the natural way. We require that (Z,Z) be isomorphic to (,) if it is infinite. We want linear orderings of Z such that, in two consecutive tuples z and z , at most two components differ, and they differ by at most 1.

We are interested in algorithms that determine the next tuple in Z by using local information, where “local” is meant with respect to certain graphs associated with Z. We want these algorithms to work as well for finite and infinite components Xi. We will formalise them by deterministic graph-walking automata and compare their enumeration powers according to the finiteness of their sets of states and the kinds of moves they can perform.

Keywords
enumeration algorithm, diagonal enumeration, graph-walking automaton, linear order
Mathematical Subject Classification 2010
Primary: 06A05, 05C38, 68R10, 68P10
Milestones
Received: 27 November 2019
Revised: 2 April 2020
Accepted: 17 April 2020
Published: 15 October 2020
Authors
Bruno Courcelle
LaBRI
University of Bordeaux and CNRS
Talence
France
Irène Durand
LaBRI
University of Bordeaux and CNRS
Talence
France
Michael Raskin
Technische Universität München
Garching bei München
Germany