There is a long and fertile interaction between research on finitestate methods and the mathematics of language: many central results in mathematical linguistics are based on finite-state models such as automata and grammars, and mathematical linguistics in turn has laid the foundations for the application of finite-state methods in natural language processing (NLP). One important outcome of the crosssemination between the two fields is the characterisation of adequate classes of string

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... s and tree languages for linguistic modelling. Our intention with this special issue is to highlight current work in the intersection between mathematics of language and finite-state methods, as presented at two premier conferences in the respective fields: the 12th International Conference on Finite-State Methods and Natural Language Processing (FSMNLP), which was held 22-24 June 2015 in Düsseldorf, Germany; and the 14th Meeting on Mathematics of Language (MOL), which was held 25-26 July 2015 in Chicago, USA. To this end we invited the authors of the two conferences to submit revised and extended versions of their contributions, which were then subjected to an entirely new peer-review process -something that would have been impossible without the dedication and thorough work of our reviewers, to whom we owe our sincere gratitude. At the end of the peer-review process, we selected four submissions for publication in this special issue: "Chomsky-Schützenberger parsing for weighted multiple contextfree languages" by Tobias Denkinger generalises the well-known char-