Syntactic complexity of prefix-, suffix-, bifix-, and factor-free regular languages
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Date
2012-08-31
Authors
Brzozowski, Janusz
Li, Baiyu
Ye, Yuli
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
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.
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/
Keywords
Bifix-free, Factor-free, Finite automaton, Monoid, Prefix-free, Regular language, Reversal, Semigroup, Suffix-free, Syntactic complexity