The tight bound on the state complexity of the reverse of R-trivial and J-trivial regular languages of the state complexity n is 2n-1. The witness is ternary for R-trivial regular languages and (n-1)-ary for J-trivial regular languages. In this paper, we prove that the bound can be met neither by a binary R-trivial regular language nor by a J-trivial regular language over an (n-2)-element alphabet. We provide a characterization of tight bounds for R-trivial regular languages depending on the state complexity of the language and the size of its alphabet. We show the tight bound for J-trivial regular languages over an (n-2)-element alphabet and a few tight bounds for binary J-trivial regular languages. The case of J-trivial regular languages over an (n-k)-element alphabet, for 2 ≤ k ≤ n-3, is open. © 2013 Springer-Verlag.
CITATION STYLE
Jirásková, G., & Masopust, T. (2013). On the state complexity of the reverse of R- and J-trivial regular languages. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8031 LNCS, pp. 136–147). https://doi.org/10.1007/978-3-642-39310-5_14
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