Show simple item record

dc.contributor.authorBrzozowski, Janusz
dc.contributor.authorDavies, Sylvie 14:44:41 (GMT) 14:44:41 (GMT)
dc.descriptionThe final publication is available at Springer via
dc.description.abstractA regular language L is non-returning if in the minimal deterministic finite automaton accepting it there are no transitions into the initial state. Eom, Han and Jirásková derived upper bounds on the state complexity of boolean operations and Kleene star, and proved that these bounds are tight using two different binary witnesses. They derived upper bounds for concatenation and reversal using three different ternary witnesses. These five witnesses use a total of six different transformations. We show that for each n⩾4 there exists a ternary witness of state complexity n that meets the bound for reversal and that at least three letters are needed to meet this bound. Moreover, the restrictions of this witness to binary alphabets meet the bounds for product, star, and boolean operations. We also derive tight upper bounds on the state complexity of binary operations that take arguments with different alphabets. We prove that the maximal syntactic semigroup of a non-returning language has (n−1)ⁿ elements and requres at least (n2) generators. We find the maximal state complexities of atoms of non-returning languages. Finally, we show that there exists a most complex non-returning language that meets the bounds for all these complexity measures.en
dc.description.sponsorshipNatural Sciences and Engineering Research Council of Canada [grant No. OGP0000871]en
dc.relation.ispartofseriesPart of the Lecture Notes in Computer Science book series (LNCS, volume 10316)en
dc.subjectBoolean operationen
dc.subjectDifferent alphabetsen
dc.subjectMost complexen
dc.subjectState complexityen
dc.subjectSyntactic semigroupen
dc.subjectTransition semigroupen
dc.subjectUnrestricted complexityen
dc.titleMost Complex Non-returning Regular Languagesen
dc.typeConference Paperen
dcterms.bibliographicCitationBrzozowski J.A., Davies S. (2017) Most Complex Non-returning Regular Languages. In: Pighizzini G., Câmpeanu C. (eds) Descriptional Complexity of Formal Systems. DCFS 2017. Lecture Notes in Computer Science, vol 10316. Springer, Chamen
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2David R. Cheriton School of Computer Scienceen

Files in this item


This item appears in the following Collection(s)

Show simple item record


University of Waterloo Library
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
519 888 4883

All items in UWSpace are protected by copyright, with all rights reserved.

DSpace software

Service outages