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Leaf languages and string compression Lohrey, Markus Leaf languages string compression grammar-based compression complexity theory Tight connections between leafs languages and strings compressed via straight-line programs (SLPs) are established. It is shown that the compressed membership problem for a language $L$ is complete for the leaf language class defined by $L$ via logspace machines. A more difficult variant of the compressed membership problem for $L$ is shown to be complete for the leaf language class defined by $L$ via polynomial time machines. As a corollary, a fixed linear visibly pushdown language with a PSPACE-complete compressed membership problem is obtained. For XML languages, the compressed membership problem is shown to be coNP-complete. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Markus Lohrey 2008 Is Part Of LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2008.1761 urn:nbn:de:0030-drops-17612 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1761 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode