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Ackermannian Integer Compression and the Word Problem for Hydra Groups Dison, Will Einstein, Eduard Riley, Timothy R. Ackermann functions hydra word problem 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Will Dison and Eduard Einstein and Timothy R. Riley 2016 Is Part Of LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2016.30 urn:nbn:de:0030-drops-64458 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.30 eng https://creativecommons.org/licenses/by/3.0/legalcode