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 ω-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.

Source : oai:HAL:hal-01196856v1

Volume: Vol. 17 no. 1

Section: Automata, Logic and Semantics

Published on: May 21, 2015

Submitted on: April 14, 2014

Keywords: set of locally positive measure,decomposition,Muller automata,</math>-language,<math>&omega,Hausdorff measure,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC]

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