# On the State Complexity of the Reverse of - and -Trivial Regular Languages

@inproceedings{Jirskov2013OnTS, title={On the State Complexity of the Reverse of - and -Trivial Regular Languages}, author={Galina Jir{\'a}skov{\'a} and Tomas Masopust}, booktitle={DCFS}, year={2013} }

The tight bound on the state complexity of the reverse of \({\mathcal R}\)-trivial and \({\mathcal J}\)-trivial regular languages of the state complexity n is 2 n − 1. The witness is ternary for \({\mathcal R}\)-trivial regular languages and (n − 1)-ary for \({\mathcal J}\)-trivial regular languages. In this paper, we prove that the bound can be met neither by a binary \({\mathcal R}\)-trivial regular language nor by a \({\mathcal J}\)-trivial regular language over an (n − 2)-element alphabet…

## 4 Citations

Quotient Complexity of Bifix-, Factor-, and Subword-free Regular Languages

- Linguistics, Computer ScienceActa Cybern.
- 2014

Tight upper bounds are found on the quotient complexity of intersection, union, difference, symmetric difference, concatenation, star, and reversal in these three classes of languages.

On Boolean combinations forming piecewise testable languages

- Mathematics, LinguisticsTheor. Comput. Sci.
- 2017

Syntactic Complexity of ℛ- and 풥-Trivial Regular Languages

- Linguistics, Computer ScienceInt. J. Found. Comput. Sci.
- 2014

It is proved that n! and ⌊e(n − 1)⌋ are tight upper bounds for the syntactic complexity of ℛ- and 𝒥-trivial regular languages, respectively.

A Survey on Operational State Complexity

- Computer ScienceJ. Autom. Lang. Comb.
- 2017

In this survey, the state complexities of individual regularity preserving language operations on regular and some subregular languages are reviewed and the combination of individual operations are revisited.

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