Abstract
The syntactic complexity of a subclass of the class of regular languages is the maximal cardinality of syntactic semigroups of languages in that class, taken as a function of the state complexity n of these languages. We prove that n! and \(\lfloor e(n-1)! \rfloor\) are tight upper bounds for the syntactic complexity of \({\mathcal R}\)- and \({\mathcal J}\)-trivial regular languages, respectively.
This work was supported by the Natural Sciences and Engineering Research Council of Canada under grant No. OGP0000871 and a Postgraduate Scholarship.
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Brzozowski, J., Li, B. (2013). Syntactic Complexity of \({\mathcal R}\)- and \({\mathcal J}\)-Trivial Regular Languages. In: Jurgensen, H., Reis, R. (eds) Descriptional Complexity of Formal Systems. DCFS 2013. Lecture Notes in Computer Science, vol 8031. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39310-5_16
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DOI: https://doi.org/10.1007/978-3-642-39310-5_16
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