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

Automata, Logic and Semantics 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 su...

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Veröffentlicht in:Discrete mathematics and theoretical computer science 2015-05, Vol.17 no. 1 (Automata, Logic and Semantics), p.357-368
1. Verfasser: Staiger, Ludwig
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Sprache:eng
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Zusammenfassung:Automata, Logic and Semantics 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.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.2112