Generic complexity of the Conjugacy Problem in HNN-extensions and algorithmic stratification of Miller's groups

Generic complexity of the Conjugacy Problem in HNN-extensions and algorithmic stratification of Miller's groups

We discuss time complexity of The Conjugacy Problem in HNN-extensions of groups, in particular, in Miller's groups. We show that for "almost all", in some explicit sense, elements, the Conjugacy Problem is decidable in cubic time. It is worth noting that the Conjugacy Problem in a Mil...

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Veröffentlicht in:arXiv.org 2009-03
Hauptverfasser: Borovik, Alexandre V, Myasnikov, Alexei G, Remeslennikov, Vladimir N
Format: Artikel
Sprache:eng
Schlagworte:
Complexity
Stratification
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Zusammenfassung:We discuss time complexity of The Conjugacy Problem in HNN-extensions of groups, in particular, in Miller's groups. We show that for "almost all", in some explicit sense, elements, the Conjugacy Problem is decidable in cubic time. It is worth noting that the Conjugacy Problem in a Miller group may have be undecidable. Our results show that "hard" instances of the problem comprise a negligibly small part of the group.
ISSN:2331-8422