We develop an algebraic theory for languages of data words. We prove that, under certain conditions, a language of data words is definable in first-order logic if and only if its syntactic monoid is aperiodic.
@InProceedings{bojanczyk:LIPIcs.STACS.2011.105, author = {Bojanczyk, Mikolaj}, title = {{Data Monoids}}, booktitle = {28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)}, pages = {105--116}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-25-5}, ISSN = {1868-8969}, year = {2011}, volume = {9}, editor = {Schwentick, Thomas and D\"{u}rr, Christoph}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2011.105}, URN = {urn:nbn:de:0030-drops-30030}, doi = {10.4230/LIPIcs.STACS.2011.105}, annote = {Keywords: Monoid, Data Words, Nominal Set, First-Order Logic} }
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