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Solutions of Word Equations Over Partially Commutative Structures Diekert, Volker Jez, Artur Kufleitner, Manfred Word equations EDT0L language trace monoid right-angled Artin group partial commutation We give NSPACE(n*log(n)) algorithms solving the following decision problems. Satisfiability: Is the given equation over a free partially commutative monoid with involution (resp. a free partially commutative group) solvable? Finiteness: Are there only finitely many solutions of such an equation? PSPACE algorithms with worse complexities for the first problem are known, but so far, a PSPACE algorithm for the second problem was out of reach. Our results are much stronger: Given such an equation, its solutions form an EDT0L language effectively representable in NSPACE(n*log(n)). In particular, we give an effective description of the set of all solutions for equations with constraints in free partially commutative monoids and groups. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Volker Diekert and Artur Jez and Manfred Kufleitner 2016 Is Part Of LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2016.127 urn:nbn:de:0030-drops-62624 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.127 eng https://creativecommons.org/licenses/by/3.0/legalcode