On the Hausdorff measure of regular ω-languages in Cantor space

Staiger, L

dc.contributor.author	Staiger, L	en
dc.date.accessioned	2015-01-05T00:14:04Z	en
dc.date.available	2015-01-05T00:14:04Z	en
dc.date.issued	2014	en
dc.identifier.citation	CDMTCS Research Reports CDMTCS-459 (2014)	en
dc.identifier.issn	1178-3540	en
dc.identifier.uri	http://hdl.handle.net/2292/23892	en
dc.description.abstract	This paper deals with the calculation of the Hausdorff measure of regular ω-languages, that is, subsets of the Cantor space definable by finite automata. Using methods for decomposing regular ω-languages into disjoint unions of parts of simple structure we derive two sufficient conditions under which !-languages with a closure definable by a finite automaton have the same Hausdorff measure as this closure. The first of these condition is related to the homogeneity of the local behaviour of the Hausdorff dimension of the underlying set, and the other with a certain topological density of the set in its closure.	en
dc.publisher	Department of Computer Science, The University of Auckland, New Zealand	en
dc.relation.ispartofseries	CDMTCS Research Report Series	en
dc.rights	Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher.	en
dc.rights.uri	https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm	en
dc.source.uri	https://www.cs.auckland.ac.nz/research/groups/CDMTCS/researchreports/index.php	en
dc.title	On the Hausdorff measure of regular ω-languages in Cantor space	en
dc.type	Technical Report	en
dc.subject.marsden	Fields of Research	en
dc.rights.holder	The author(s)	en
dc.rights.accessrights	http://purl.org/eprint/accessRights/OpenAccess	en
dc.relation.isnodouble	6111	*