Syntactic Complexities of Six Classes of Star-Free Languages
MetadataShow full item record
The syntactic complexity of a regular language is the cardinality of its syntactic semi-group. The syntactic complexity of a subclass of regular languages is the maximal syntactic complexity of languages in that subclass, taken as a function of the state complexity n of these languages. We study the syntactic complexity of six subclasses of star-free languages. We ﬁnd a tight upper bound of (n−1)! for ﬁnite/coﬁnite and re-verse deﬁnite languages, and a lower bound of ⌊e·(n−1)!⌋ for deﬁnite languages, where e is the base of the natural logarithms. We also ﬁnd tight upper bounds for languages accepted by monotonic, partially monotonic and “nearly monotonic” automata. All these bounds are signiﬁcantly lower than the bound nn for arbitrary regular languages. Also, witness languages reaching these bounds require alphabets that grow with n. The syntactic complexity of arbitrary star-free languages remains open.
Cite this work
Janusz Brzozowski, Baiyu Li, David Liu (2012). Syntactic Complexities of Six Classes of Star-Free Languages. UWSpace. http://hdl.handle.net/10012/12625
Showing items related by title, author, creator and subject.
Online Digital Game-Based Language Learning Environments: Opportunities for Second Language Development Scholz, Kyle (University of Waterloo, 2016-01-07)This dissertation project is an analysis of the language learning processes of 14 learners playing in and interacting with the massive multiplayer online role-playing game (MMORPG) World of Warcraft (WoW) in German in order ...
Penner, Nikolai (University of Waterloo, 2010-01-20)The main focus of this study is the High German language spoken by Russian Mennonites, one of the many groups of German-speaking immigrants in Canada. Although the primary language of most Russian Mennonites is a Low German ...
Pollon, Simon Carl (University of Waterloo, 2007-09-27)There exists a broad inclination among those who theorize about mental representation to assume that the meanings of linguistic units, like words, are going to be identical to, and work exactly like, mental representations, ...