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dc.contributor.authorBrzozowski, Janusz
dc.contributor.authorSinnamon, Corwin 14:08:55 (GMT) 14:08:55 (GMT)
dc.descriptionThis is an Accepted Manuscript of an article published by Institut für Informatik in Journal of Automata, Languages and Combinatorics on 2017-08-27, available online:
dc.description.abstractWe study the state complexity of binary operations on regular languages over different alphabets. It is known that if L′m and Ln are languages of state complexities m and n, respectively, and restricted to the same alphabet, the state complexity of any binary boolean operation on L′m and Ln is mn, and that of product (concatenation) is m2n − 2n−1. In contrast to this, we show that if L′m and Ln are over different alphabets, the state complexity of union and symmetric difference is (m + 1)(n + 1), that of difference is mn + m, that of intersection is mn, and that of product is m2n + 2n−1. We also study unrestricted complexity of binary operations in the classes of regular right, left, and two-sided ideals, and derive tight upper bounds. The bounds for product of the unrestricted cases (with the bounds for the restricted cases in parentheses) are as follows: right ideals m + 2n−2 + 2n−1 + 1 (m + 2n−2); left ideals mn + m + n (m + n − 1); two-sided ideals m+2n (m+n−1). The state complexities of boolean operations on all three types of ideals are the same as those of arbitrary regular languages, whereas that is not the case if the alphabets of the arguments are the same. Finally, we update the known results about most complex regular, right-ideal, left-ideal, and two-sided-ideal languages to include the unrestricted cases.en
dc.description.sponsorshipNatural Sciences and Engineering Research Council of Canada grant No. OGP0000871en
dc.publisherInstitut für Informatiken
dc.subjectBoolean operationen
dc.subjectDifferent alphabetsen
dc.subjectLeft idealen
dc.subjectMost complex languageen
dc.subjectQuotient complexityen
dc.subjectRegular languageen
dc.subjectRight idealen
dc.subjectState complexityen
dc.subjectTwo-sided idealen
dc.subjectUnrestricted complexityen
dc.titleUnrestricted State Complexity Of Binary Operations On Regular And Ideal Languagesen
dc.typeConference Paperen
dcterms.bibliographicCitationBrzozowski, J. A, Sinnamon, C (2017) Unrestricted State Complexity of Binary Operations on Regular and Ideal Languages. Journal of Automata, Languages and Combinatorics (22) 1–3, 29–59.en
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2David R. Cheriton School of Computer Scienceen

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