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arXiv · 1208.4650

Syntactic Complexity of R- and J-Trivial Regular Languages

Janusz Brzozowski·Baiyu Li
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Abstract

The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of the class of regular languages is the maximal syntactic complexity of languages in that class, taken as a function of the state complexity n of these languages. We study the syntactic complexity of R- and J-trivial regular languages, and prove that n! and floor of [e(n-1)!] are tight upper bounds for these languages, respectively. We also prove that 2^{n-1} is the tight upper bound on the state complexity of reversal of J-trivial regular languages.

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Janusz Brzozowski, Baiyu Li. 2012-08-23. Syntactic Complexity of R- and J-Trivial Regular Languages. https://arxiv.org/abs/1208.4650

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