Show simple item record

dc.contributor.authorBrzozowski, Janusz
dc.contributor.authorTamm, Hellis 14:03:09 (GMT) 14:03:09 (GMT)
dc.descriptionElectronic version of an article published as International Journal of Foundations of Computer Science, 24(07), 2013, 1009–1027. © World Scientific Publishing Company
dc.description.abstractThe quotient complexity of a regular language L, which is the same as its state complexity the number of left quotients of L. An atom of a non-empty regular language L with n quotients is a non-empty intersection of the n quotients, which can be uncomplemented or complemented. An NFA is atomic if the right language of every state is a union of atoms. We characterize all reduced atomic NFAs of a given language, i.e., those NFAs that have no equivalent states, We prove that, for any language L with quotient complexity n, the quotient complexity of any atom of L with r complemented quotients has an upper bound of 2(n) - 1 if r = 0 or r = n; for 1 <= r <= n - 1 the bound is 1+ (k=1)Sigma(r) (h=k+1)Sigma(k+n-r) ((n)(h)) ((h)(k)). For each n >= 2 we exhibit a language with 2(n) atoms which meet these bounds.en
dc.description.sponsorshipNatural Sciences and Engineering Research Council of Canada [OGP0000871]en
dc.description.sponsorshipEstonian Science Foundation [7520]en
dc.description.sponsorshipEstonian Ministry of Education and Research [0140007s12]en
dc.publisherWorld Scientific Publishingen
dc.subjectfinite automatonen
dc.subjectatomic NFAen
dc.subjectquotient complexityen
dc.subjectregular languageen
dc.subjectstate complexityen
dc.subjectsyntactic semigroupen
dc.titleComplexity Of Atoms Of Regular Languagesen
dcterms.bibliographicCitationBrzozowski, J., & Tamm, H. (2013). COMPLEXITY OF ATOMS OF REGULAR LANGUAGES. International Journal of Foundations of Computer Science, 24(07), 1009–1027.
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