Syntactic Complexity of Ideal and Closed Languages
نویسندگان
چکیده
The state complexity of a regular language is the number of states in the minimal deterministic automaton accepting the language. 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 worst-case syntactic complexity taken as a function of the state complexity n of languages in that class. We study the syntactic complexity of the class of regular ideal languages and their complements, the closed languages. We prove that n is a tight upper bound on the complexity of right ideals and prefix-closed languages, and that there exist left ideals and suffix-closed languages of syntactic complexity n + n − 1, and two-sided ideals and factor-closed languages of syntactic complexity n + (n− 2)2 + 1.
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