Syntactic Complexities of Some Classes of Star-Free Languages
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The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. 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 three subclasses of star-free languages. We find tight upper bounds for languages accepted by monotonic, partially monotonic and “nearly monotonic” automata; all three of these classes are star-free. We conjecture that the bound for nearly monotonic languages is also a tight upper bound for star-free languages.
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Janusz Brzozowski, Baiyu Li (2012). Syntactic Complexities of Some Classes of Star-Free Languages. UWSpace. http://hdl.handle.net/10012/12508