Syntactic Complexity of Suffix-Free Languages
| dc.contributor.author | Brzozowski, Janusz | |
| dc.contributor.author | Szykuła, Marek | |
| dc.date.accessioned | 2017-09-28T14:08:56Z | |
| dc.date.available | 2017-09-28T14:08:56Z | |
| dc.date.issued | 2017-09-05 | |
| dc.description | The final publication is available at Elsevier via http://dx.doi.org/10.1016/j.ic.2017.08.014 © 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ | en |
| dc.description.abstract | We solve an open problem concerning syntactic complexity: We prove that the cardinality of the syntactic semigroup of a suffix-free language with n left quotients (that is, with state complexity n) is at most (n−1)n−2+n−2 for n⩾6. Since this bound is known to be reachable, this settles the problem. We also reduce the alphabet of the witness languages reaching this bound to five letters instead of n+2, and show that it cannot be any smaller. Finally, we prove that the transition semigroup of a minimal deterministic automaton accepting a witness language is unique for each n. | en |
| dc.description.sponsorship | Natural Sciences and Engineering Research Council of Canada (NSERC) grant No. OGP000087 | en |
| dc.description.sponsorship | National Science Centre, Poland project number 2014/15/B/ST6/00615 | en |
| dc.identifier.uri | http://dx.doi.org/10.1016/j.ic.2017.08.014 | |
| dc.identifier.uri | http://hdl.handle.net/10012/12500 | |
| dc.language.iso | en | en |
| dc.publisher | Elsevier | en |
| dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | * |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
| dc.subject | Regular language | en |
| dc.subject | Suffix-free | en |
| dc.subject | Syntactic complexity | en |
| dc.subject | Transition semigroup | en |
| dc.subject | Upper bound | en |
| dc.title | Syntactic Complexity of Suffix-Free Languages | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Brzozowski, J. A., & Szykuła, M. (2017). Syntactic complexity of suffix-free languages. Information and Computation. https://doi.org/10.1016/j.ic.2017.08.014 | en |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.contributor.affiliation2 | David R. Cheriton School of Computer Science | en |
| uws.peerReviewStatus | Reviewed | en |
| uws.scholarLevel | Faculty | en |
| uws.typeOfResource | Text | en |