Syntactic complexity of prefix-, suffix-, bifix-, and factor-free regular languages
| dc.contributor.author | Brzozowski, Janusz | |
| dc.contributor.author | Li, Baiyu | |
| dc.contributor.author | Ye, Yuli | |
| dc.date.accessioned | 2017-11-13T22:52:27Z | |
| dc.date.available | 2017-11-13T22:52:27Z | |
| dc.date.issued | 2012-08-31 | |
| dc.description | The final publication is available at Elsevier via http://dx.doi.org/10.1016/j.tcs.2012.04.011 © 2012. 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 | The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of the class of regular languages is the maximal syntactic complexity of languages in that class, taken as a function of the state complexity n of these languages. We study the syntactic complexity of prefix-, suffix-, bifix-, and factor-free regular languages. We prove that n(n-2) is a tight upper bound for prefix-free regular languages. We present properties of the syntactic semigroups of suffix-, bifix-, and factor-free regular languages, conjecture tight upper bounds on their size to be (n-1)(n-2) + (n-2), (n - 1)(n-3) + (n - 2)(n-3) + (n - 3)(n-3), and (n - 1)(n-3) + (n - 3)2(n-3) + 1, respectively, and exhibit languages with these syntactic complexities. (C) 2012 Elsevier B.V. All rights reserved. | en |
| dc.description.sponsorship | Natural Sciences and Engineering Research Council of Canada [OGP0000871] | en |
| dc.description.sponsorship | Department of Computer Science, University of Toronto | en |
| dc.identifier.uri | http://dx.doi.org/10.1016/j.tcs.2012.04.011 | |
| dc.identifier.uri | http://hdl.handle.net/10012/12622 | |
| 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 | Bifix-free | en |
| dc.subject | Factor-free | en |
| dc.subject | Finite automaton | en |
| dc.subject | Monoid | en |
| dc.subject | Prefix-free | en |
| dc.subject | Regular language | en |
| dc.subject | Reversal | en |
| dc.subject | Semigroup | en |
| dc.subject | Suffix-free | en |
| dc.subject | Syntactic complexity | en |
| dc.title | Syntactic complexity of prefix-, suffix-, bifix-, and factor-free regular languages | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Brzozowski, J., Li, B., & Ye, Y. (2012). Syntactic complexity of prefix-, suffix-, bifix-, and factor-free regular languages. Theoretical Computer Science, 449(Supplement C), 37–53. https://doi.org/10.1016/j.tcs.2012.04.011 | 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 |