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@article{1642039, author = {Meneses Guimaräes de Almeida, Jorge Manuel and Klíma, Ondřej}, article_location = {NANCY}, article_number = {3}, keywords = {Regular language; polynomial closure; pseudovariety; finite ordered monoid; pseudoidentity; Burnside pseudovariety}, language = {eng}, issn = {1462-7264}, journal = {DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE}, title = {On the insertion of n-powers}, url = {https://dmtcs.episciences.org/5155}, volume = {21}, year = {2019} }
TY - JOUR ID - 1642039 AU - Meneses Guimaräes de Almeida, Jorge Manuel - Klíma, Ondřej PY - 2019 TI - On the insertion of n-powers JF - DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE VL - 21 IS - 3 SP - 1-18 EP - 1-18 PB - DISCRETE MATHEMATICS THEORETICAL COMPUTER SCIENCE SN - 14627264 KW - Regular language KW - polynomial closure KW - pseudovariety KW - finite ordered monoid KW - pseudoidentity KW - Burnside pseudovariety UR - https://dmtcs.episciences.org/5155 L2 - https://dmtcs.episciences.org/5155 N2 - In algebraic terms, the insertion of n-powers in words may be modelled at the language level by considering the pseudovariety of ordered monoids defined by the inequality 1 <= x(n). We compare this pseudovariety with several other natural pseudovarieties of ordered monoids and of monoids associated with the Burnside pseudovariety of groups defined by the identity x(n) = 1. In particular, we are interested in determining the pseudovariety of monoids that it generates, which can be viewed as the problem of determining the Boolean closure of the class of regular languages closed under n-power insertions. We exhibit a simple upper bound and show that it satisfies all pseudoidentities which are provable from 1 <= x(n) in which both sides are regular elements with respect to the upper bound. ER -
MENESES GUIMARÄES DE ALMEIDA, Jorge Manuel a Ondřej KLÍMA. On the insertion of n-powers. \textit{DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE}. NANCY: DISCRETE MATHEMATICS THEORETICAL COMPUTER SCIENCE, 2019, roč.~21, č.~3, s.~1-18. ISSN~1462-7264.
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