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dc.contributor.authorBrzozowski, Janusz 14:03:10 (GMT) 14:03:10 (GMT)
dc.descriptionElectronic version of an article published as International Journal of Foundations of Computer Science, 24(06), 2013, 691–708. © World Scientific Publishing Company
dc.description.abstractSequences (L-n vertical bar n >= k), called streams, of regular languages L-n are considered, where k is some small positive integer, n is the state complexity of L-n, and the languages in a stream differ only in the parameter n, but otherwise, have the same properties. The following measures of complexity are proposed for any stream: (1) the state complexity n of L-n, that is the number of left quotients of L-n (used as a reference); (2) the state complexities of the left, quotients of L-n; (3) the number of atoms of L-n; (4) the state complexities of the atoms of L-n; (5) the size of the syntactic semigroup of L; and the state complexities of the following operations: (6) the reverse of L-n; (7) the star; (8) union, intersection, difference and symmetric difference of and L-n; and the concatenation of L-m and L-n. A stream that has the highest possible complexity with respect to these measures is then viewed as a most complex stream. The language stream (U-n (a, b, c) vertical bar n >= 3 is defined by the deterministic finite automaton with state set {0, 1, ..., n-1}, initial state 0, set {n-1} of final states, and input alphabet {a, b, c}, where a performs a cyclic permutation of the;a states, b transposes states 0 and 1, and c maps state n - 1 to state 0. This stream achieves the highest possible complexities with the exception of boolean operations where m = n. In the latter case, one can use U-n (a, b, c) and U-n(a, b, c), where the roles of a and b are interchanged in the second language. In this sense, U-n (a, b, c) is a universal witness This witness and its extensions also apply to a large number of combined regular operations.en
dc.description.sponsorshipNatural Sciences and Engineering Research Council of Canada [OGP0000871]en
dc.publisherWorld Scientific Publishingen
dc.subjectcomplexity of operationen
dc.subjectfinite automatonen
dc.subjectquotient complexityen
dc.subjectregular languageen
dc.subjectstate complexityen
dc.subjectsyntactic semigroupen
dc.titleIn Search Of Most Complex Regular Languagesen
dcterms.bibliographicCitationBrzozowski, J. (2013). IN SEARCH OF MOST COMPLEX REGULAR LANGUAGES. International Journal of Foundations of Computer Science, 24(06), 691–708.
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2David R. Cheriton School of Computer Scienceen

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