Sciweavers

FUN
2007
Springer

Die Another Day

13 years 9 months ago
Die Another Day
The Hydra was a many-headed monster from Greek mythology that would immediately replace a head that was cut off by one or two new heads. It was the ask of Hercules to kill this monster. In an abstract sense, a Hydra can be modeled as a tree where the leaves are the heads, and when a head is cut off some subtrees get duplicated. Different Hydra species differ by which subtress can be duplicated in which multiplicity. Using some deep mathematics, it had been shown that two classes of Hydra species must always die, independent of the order in which heads are cut off. In this paper we identify three properties for a Hydra that are necessary and sufficient to make it immortal or force it to die. We also give a simple combinatorial proof for this classification. Now, if Hercules had known this... Keywords Hydra battle · Buchholz Hydra · Peano arithmetic · PA · Koenig’s lemma · Transfinite induction
Rudolf Fleischer
Added 07 Jun 2010
Updated 07 Jun 2010
Type Conference
Year 2007
Where FUN
Authors Rudolf Fleischer
Comments (0)