eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-08-19
30:1
30:14
10.4230/LIPIcs.MFCS.2016.30
article
Ackermannian Integer Compression and the Word Problem for Hydra Groups
Dison, Will
Einstein, Eduard
Riley, Timothy R.
For a finitely presented group, the word problem asks for an algorithm which declares whether or not words on the generators represent the identity. The Dehn function is a complexity measure of a direct attack on the word problem by applying the defining relations. Dison and Riley showed that a "hydra phenomenon" gives rise to novel groups with extremely fast growing (Ackermannian) Dehn functions. Here we show that nevertheless, there are efficient (polynomial time) solutions to the word problems of these groups. Our main innovation is a means of computing efficiently with enormous integers which are represented in compressed forms by strings of Ackermann functions.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol058-mfcs2016/LIPIcs.MFCS.2016.30/LIPIcs.MFCS.2016.30.pdf
Ackermann functions
hydra
word problem