Abstract
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 prove that n n − 1 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 + n − 1, and two-sided ideals and factor-closed languages of syntactic complexity n n − 2 + (n − 2)2n − 2 + 1.
This work was supported by the Natural Sciences and Engineering Research Council of Canada under grant No. OGP0000871 and a Postgraduate Scholarship, and by a Graduate Award from the Department of Computer Science, University of Toronto.
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Brzozowski, J., Ye, Y. (2011). Syntactic Complexity of Ideal and Closed Languages. In: Mauri, G., Leporati, A. (eds) Developments in Language Theory. DLT 2011. Lecture Notes in Computer Science, vol 6795. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22321-1_11
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