Geometrical Closure of Binary \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{3/2}$$\end{document} Languages

• Published in: Language and Automata Theory and Applications pp. 302 - 314
• Main Authors: Dubernard, Jean-Philippe, Guaiana, Giovanna, Mignot, Ludovic
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Geometrical language; Regular expression; Regular language; Straubing-Thérien hierarchy
• ISBN: 9783030134341; 3030134342
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-13435-8_22

We define the geometrical closure of a language over a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$j$$\end{document}-ary alphabet, and we prove that in the case of dimension 2 the family \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{3/2}$$\end{document} in the Straubing-Thérien hierarchy of languages is closed under this operation. In other words, the geometrical closure of a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{3/2}$$\end{document} binary language is still a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{3/2}$$\end{document} language. This is achieved by carrying out some transformations over a regular expression representing the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{3/2}$$\end{document} language, which leads to a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{3/2}$$\end{document} regular expression for the geometrical closure.