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Some natural decision problems in automatic graphs

Published online by Cambridge University Press:  12 March 2014

Dietrich Kuske and
Markus Lohrey
Dietrich Kuske
Affiliation:
Labri, CNRS, Université Bordeaux I, 351, Cours de la Libération F-33405 Talence, France. E-mail: kuske@labri.fr
Markus Lohrey
Affiliation:
Universität Leipzig, Institut für Informatik Postfach 100920, D-04009 Leipzig, Germany. E-mail: lohrey@informatik.uni-Leipzig.de
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Abstract

For automatic and recursive graphs, we investigate the following problems:

(A) existence of a Hamiltonian path and existence of an infinite path in a tree

(B) existence of an Euler path, bounding the number of ends, and bounding the number of infinite branches in a tree

(C) existence of an infinite clique and an infinite version of set cover

The complexity of these problems is determined for automatic graphs and. supplementing results from the literature, for recursive graphs. Our results show that these problems

(A) are equally complex for automatic and for recursive graphs (-complete).

(B) are moderately less complex for automatic than for recursive graphs (complete for different levels of the arithmetic hierarchy),

(C) are much simpler for automatic than for recursive graphs (decidable and -complete, resp.).

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 2 , June 2010, pp. 678 - 710
Copyright
Copyright © Association for Symbolic Logic 2010

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