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Quotient Complexities of Atoms in Regular Ideal Languages
dc.contributor.author | Brzozowski, Janusz | |
dc.contributor.author | Davies, Sylvie | |
dc.date.accessioned | 2017-10-05 16:58:17 (GMT) | |
dc.date.available | 2017-10-05 16:58:17 (GMT) | |
dc.date.issued | 2015 | |
dc.identifier.uri | http://dx.doi.org/10.14232/actacyb.22.2.2015.4 | |
dc.identifier.uri | http://hdl.handle.net/10012/12531 | |
dc.description.abstract | A (left) quotient of a language L by a word w is the language w(-1) L = {x vertical bar wx is an element of L}. The quotient complexity of a regular language L is the number of quotients of L; it is equal to the state complexity of L, which is the number of states in a minimal deterministic finite automaton accepting L. An atom of L is an equivalence class of the relation in which two words are equivalent if for each quotient, they either are both in the quotient or both not in it; hence it is a non-empty intersection of complemented and uncomplemented quotients of L. A right (respectively, left and two-sided) ideal is a language L over an alphabet Sigma that satisfies L = L Sigma* (respectively, L = Sigma*L and L = Sigma*L Sigma*). We compute the maximal number of atoms and the maximal quotient complexities of atoms of right, left and two-sided regular ideals. | en |
dc.description.sponsorship | Natural Sciences and Engineering Research Council of Canada [OGP0000871] | en |
dc.language.iso | en | en |
dc.publisher | Institute of Informatics: University of Szeged | en |
dc.subject | atom | en |
dc.subject | left ideal | en |
dc.subject | quotient | en |
dc.subject | quotient complexity | en |
dc.subject | regular language | en |
dc.subject | right ideal | en |
dc.subject | state complexity | en |
dc.subject | syntactic semigroup | en |
dc.subject | two-sided ideal | en |
dc.title | Quotient Complexities of Atoms in Regular Ideal Languages | en |
dc.type | Article | en |
dcterms.bibliographicCitation | Brzozowski, J., & Davies, S. (2015). Quotient Complexities of Atoms in Regular Ideal Languages. Acta Cybernetica, 22(2), 293–311. https://doi.org/10.14232/actacyb.22.2.2015.4 | 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 |