Brzozowski, JanuszLi, BaiyuYe, Yuli2017-11-132017-11-132012-08-31http://dx.doi.org/10.1016/j.tcs.2012.04.011http://hdl.handle.net/10012/12622The 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/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.enAttribution-NonCommercial-NoDerivatives 4.0 InternationalBifix-freeFactor-freeFinite automatonMonoidPrefix-freeRegular languageReversalSemigroupSuffix-freeSyntactic complexityArticle