2026-07-24T01:23:54Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:16870 2024-03-06T10:58:33Z ddc:004 open_access

Streaming Word Problems Lohrey, Markus Lück, Lukas word problems for groups streaming algorithms We study deterministic and randomized streaming algorithms for word problems of finitely generated groups. For finitely generated linear groups, metabelian groups and free solvable groups we show the existence of randomized streaming algorithms with logarithmic space complexity for their word problems. We also show that the class of finitely generated groups with a logspace randomized streaming algorithm for the word problem is closed under several group theoretical constructions: finite extensions, direct products, free products and wreath products by free abelian groups. We contrast these results with several lower bound. An example of a finitely presented group, where the word problem has only a linear space randomized streaming algorithm, is Thompson’s group F. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Markus Lohrey and Lukas Lück 2022 Is Part Of LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2022.72 urn:nbn:de:0030-drops-168707 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.72 eng https://creativecommons.org/licenses/by/4.0/legalcode