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Automatic linear orders and trees

Automatic linear orders and trees We investigate partial orders that are computable, in a precise sense, by finite automata. Our emphasis is on trees and linear orders. We study the relationship between automatic linear orders and trees in terms of rank functions that are related to Cantor--Bendixson rank. We prove that automatic linear orders and automatic trees have finite rank. As an application we provide a procedure for deciding the isomorphism problem for automatic ordinals. We also investigate the complexity and definability of infinite paths in automatic trees. In particular, we show that every infinite path in an automatic tree with countably many infinite paths is a regular language. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

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References (20)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2005 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/1094622.1094625
Publisher site
See Article on Publisher Site

Abstract

We investigate partial orders that are computable, in a precise sense, by finite automata. Our emphasis is on trees and linear orders. We study the relationship between automatic linear orders and trees in terms of rank functions that are related to Cantor--Bendixson rank. We prove that automatic linear orders and automatic trees have finite rank. As an application we provide a procedure for deciding the isomorphism problem for automatic ordinals. We also investigate the complexity and definability of infinite paths in automatic trees. In particular, we show that every infinite path in an automatic tree with countably many infinite paths is a regular language.

Journal

ACM Transactions on Computational Logic (TOCL)Association for Computing Machinery

Published: Oct 1, 2005

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