dc.contributor.author Brzozowski, Janusz dc.date.accessioned 2017-09-29 14:03:10 (GMT) dc.date.available 2017-09-29 14:03:10 (GMT) dc.date.issued 2013-09-01 dc.identifier.uri http://dx.doi.org/10.1142/S0129054113400133 dc.identifier.uri http://hdl.handle.net/10012/12514 dc.description Electronic version of an article published as International Journal of Foundations of Computer Science, 24(06), 2013, 691–708. http://dx.doi.org/10.1142/S0129054113400133 © World Scientific Publishing Company http://www.worldscientific.com/ en dc.description.abstract Sequences (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.sponsorship Natural Sciences and Engineering Research Council of Canada [OGP0000871] en dc.language.iso en en dc.publisher World Scientific Publishing en dc.subject Atom en dc.subject complexity of operation en dc.subject finite automaton en dc.subject quotient complexity en dc.subject regular language en dc.subject state complexity en dc.subject syntactic semigroup en dc.subject Witness en dc.title In Search Of Most Complex Regular Languages en dc.type Article en dcterms.bibliographicCitation Brzozowski, J. (2013). IN SEARCH OF MOST COMPLEX REGULAR LANGUAGES. International Journal of Foundations of Computer Science, 24(06), 691–708. https://doi.org/10.1142/S0129054113400133 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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