Abstract
We define the geometrical closure of a language over a (Formula Presented)-ary alphabet, and we prove that in the case of dimension 2 the family (Formula Presented) in the Straubing-Thérien hierarchy of languages is closed under this operation. In other words, the geometrical closure of a (Formula Presented) binary language is still a (Formula Presented) language. This is achieved by carrying out some transformations over a regular expression representing the (Formula Presented) language, which leads to a (Formula Presented) regular expression for the geometrical closure.
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Dubernard, J. P., Guaiana, G., & Mignot, L. (2019). Geometrical Closure of Binary V3/2 Languages. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11417 LNCS, pp. 302–314). Springer Verlag. https://doi.org/10.1007/978-3-030-13435-8_22
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