# Unary Prime Languages

@inproceedings{Jecker2020UnaryPL, title={Unary Prime Languages}, author={Isma{\"e}l Jecker and Orna Kupferman and Nicolas Mazzocchi}, booktitle={MFCS}, year={2020} }

11 A regular language L of finite words is composite if there are regular languages L1, L2, . . . , Lt such 12 that L = ⋂t i=1 Li and the index (number of states in a minimal DFA) of every language Li is strictly 13 smaller than the index of L. Otherwise, L is prime. Primality of regular languages was introduced 14 and studied in [9], where the complexity of deciding the primality of the language of a given DFA 15 was left open, with a doubly-exponential gap between the upper and lower bounds…

## 2 Citations

Usefulness of information and decomposability of unary regular languages

- Computer ScienceInformation and Computation
- 2022

Decomposing Permutation Automata

- Computer Science, MathematicsCONCUR
- 2021

An NP algorithm is provided to decide whether a permutation DFA is composite, and it is shown that, for commutative permutation DFAs, restricting the number of factors makes the decision computationally harder, and yields a problem with tight bounds: it is NP-complete.

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