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The Power Word Problem Lohrey, Markus Weiß, Armin word problem compressed word problem free groups In this work we introduce a new succinct variant of the word problem in a finitely generated group G, which we call the power word problem: the input word may contain powers p^x, where p is a finite word over generators of G and x is a binary encoded integer. The power word problem is a restriction of the compressed word problem, where the input word is represented by a straight-line program (i.e., an algebraic circuit over G). The main result of the paper states that the power word problem for a finitely generated free group F is AC^0-Turing-reducible to the word problem for F. Moreover, the following hardness result is shown: For a wreath product G Wr Z, where G is either free of rank at least two or finite non-solvable, the power word problem is complete for coNP. This contrasts with the situation where G is abelian: then the power word problem is shown to be in TC^0. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Markus Lohrey and Armin Weiß 2019 Is Part Of LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2019.43 urn:nbn:de:0030-drops-109871 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.43 eng https://creativecommons.org/licenses/by/3.0/legalcode