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For a number [Formula: see text] and an [Formula: see text]-ary regularity preserving operation \u2218, we define [Formula: see text] as the set of all integers [Formula: see text] such that there are [Formula: see text]\u00a0languages [Formula: see text], [Formula: see text], with [Formula: see text] In this paper, we study these sets for the operations union, catenation, star, complement, set-subtraction, and intersection where we restrict to unary or finite or unary and finite languages [Formula: see text].<\/jats:p>","DOI":"10.1142\/s0129054119400240","type":"journal-article","created":{"date-parts":[[2019,9,19]],"date-time":"2019-09-19T07:06:43Z","timestamp":1568876803000},"page":"959-978","source":"Crossref","is-referenced-by-count":0,"title":["Operational Accepting State Complexity: The Unary and Finite Case"],"prefix":"10.1142","volume":"30","author":[{"given":"J\u00fcrgen","family":"Dassow","sequence":"first","affiliation":[{"name":"Fakult\u00e4t f\u00fcr Informatik, Otto-von-Guericke-Universit\u00e4t Magdeburg, PSF 4120, 39016 Magdeburg, Germany"}]}],"member":"219","published-online":{"date-parts":[[2019,9,19]]},"reference":[{"key":"S0129054119400240BIB001","doi-asserted-by":"publisher","DOI":"10.4204\/EPTCS.252.8"},{"key":"S0129054119400240BIB003","first-page":"71","volume":"15","author":"Brzozowski J.","year":"2010","journal-title":"Journal of Automata, Languages, and Combinatorics"},{"key":"S0129054119400240BIB005","first-page":"55","volume":"21","author":"Dassow J.","year":"2016","journal-title":"Journal of Automata, Languages, and Combinatorics"},{"key":"S0129054119400240BIB006","first-page":"123","volume":"17","author":"Dassow J.","year":"2012","journal-title":"Journal of Automata, Languages, and Combinatorics"},{"key":"S0129054119400240BIB007","first-page":"35","volume":"83","author":"Dassow J.","year":"2008","journal-title":"Fundamenta Informaticae"},{"key":"S0129054119400240BIB008","doi-asserted-by":"publisher","DOI":"10.3233\/FI-2017-1577"},{"key":"S0129054119400240BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/11691617_1"},{"key":"S0129054119400240BIB010","first-page":"251","volume":"21","author":"Gao Y.","year":"2016","journal-title":"Journal of Automata, Languages and Combinatorics"},{"key":"S0129054119400240BIB011","doi-asserted-by":"crossref","first-page":"143","DOI":"10.3233\/FI-2011-533","volume":"110","author":"Gao Y.","year":"2011","journal-title":"Fundamenta Informaticae"},{"key":"S0129054119400240BIB012","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054103002199"},{"key":"S0129054119400240BIB013","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054109006747"},{"key":"S0129054119400240BIB014","first-page":"170","volume-title":"Proc. 7th Intern. 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