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2020 On defining linear orders by automata
Bruno Courcelle, Irène Durand, Michael Raskin
Mosc. J. Comb. Number Theory 9(3): 253-291 (2020). DOI: 10.2140/moscow.2020.9.253

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.

Citation

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Bruno Courcelle. Irène Durand. Michael Raskin. "On defining linear orders by automata." Mosc. J. Comb. Number Theory 9 (3) 253 - 291, 2020. https://doi.org/10.2140/moscow.2020.9.253

Information

Received: 27 November 2019; Revised: 2 April 2020; Accepted: 17 April 2020; Published: 2020
First available in Project Euclid: 22 October 2020

zbMATH: 07272349
MathSciNet: MR4164869
Digital Object Identifier: 10.2140/moscow.2020.9.253

Subjects:
Primary: 05C38, 06A05, 68P10, 68R10

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.9 • No. 3 • 2020
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