dc.contributor.author Brzozowski, Janusz dc.contributor.author Sinnamon, Corwin dc.date.accessioned 2017-09-28 14:08:55 (GMT) dc.date.available 2017-09-28 14:08:55 (GMT) dc.date.issued 2017-08-27 dc.identifier.uri http://www.jalc.de/issues/issue_22_1-3/content.html dc.identifier.uri http://hdl.handle.net/10012/12498 dc.description This 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: http://www.jalc.de/issues/issue_22_1-3/content.html en dc.description.abstract We 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.sponsorship Natural Sciences and Engineering Research Council of Canada grant No. OGP0000871 en dc.language.iso en en dc.publisher Institut für Informatik en dc.subject Boolean operation en dc.subject Concatenation en dc.subject Different alphabets en dc.subject Left ideal en dc.subject Most complex language en dc.subject Product en dc.subject Quotient complexity en dc.subject Regular language en dc.subject Right ideal en dc.subject State complexity en dc.subject Sream en dc.subject Two-sided ideal en dc.subject Unrestricted complexity en dc.title Unrestricted State Complexity Of Binary Operations On Regular And Ideal Languages en dc.type Conference Paper en dcterms.bibliographicCitation Brzozowski, 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.affiliation1 Faculty of Mathematics en uws.contributor.affiliation2 David R. Cheriton School of Computer Science en uws.typeOfResource Text en uws.peerReviewStatus Reviewed en uws.scholarLevel Faculty en
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