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Fleischer, Rudolf

Die Another Day

06091.FleischerRudolf.Paper.765.pdf (0.2 MB)


The hydra was a many-headed monster from Greek mythology that could grow one or two new heads when one of its heads got cut off. It was the second task of Hercules to kill this monster. In an abstract sense a hydra can be modeled by a tree where the leaves are the heads, and when a head is cut off some subtrees get duplicated. Different hydra species differ by the location of subtrees to be duplicated and by the number of new subtrees grown in each step. Using some deep mathematics, it had been shown that two classes of rather restricted hydra species must always die, independent of the order in which heads are cut off. In this paper we provide an elementary proof which actually gives a complete classification of all hydra species as immortal or doomed. Now, if Hercules had known this...

BibTeX - Entry

  author =	{Rudolf Fleischer},
  title =	{Die Another Day},
  booktitle =	{Data Structures},
  year =	{2006},
  editor =	{Lars Arge and Robert Sedgewick and Dorothea Wagner},
  number =	{06091},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{},
  annote =	{Keywords: Hydra, Koenig's Lemma, Peano Arithmetic}

Keywords: Hydra, Koenig's Lemma, Peano Arithmetic
Seminar: 06091 - Data Structures
Issue Date: 2006
Date of publication: 30.11.2006

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