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- W4287714446 abstract "We give a new characterization of primitive permutation groups tied to the notion of completely reachable automata. Also, we introduce sync-maximal permutation groups tied to the state complexity of the set of synchronizing words of certain associated automata and show that they are contained between the $2$-homogeneous and the primitive groups. Lastly, we define $k$-reachable groups in analogy with synchronizing groups and motivated by our characterization of primitive permutation groups. But the results show that a $k$-reachable permutation group of degree $n$ with $6 le k le n - 6$ is either the alternating or the symmetric group." @default.
- W4287714446 created "2022-07-26" @default.
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- W4287714446 date "2020-07-17" @default.
- W4287714446 modified "2023-10-16" @default.
- W4287714446 title "Completely Reachable Automata, Primitive Groups and the State Complexity of the Set of Synchronizing Words" @default.
- W4287714446 doi "https://doi.org/10.48550/arxiv.2007.09104" @default.
- W4287714446 hasPublicationYear "2020" @default.
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