On the Synchronization of Circular Semi-Flower Automata
Formal Languages and Automata Theory
2018-08-07 v1
Abstract
Pin proved that every circular automaton with a prime number of states containing a non-permutation is synchronizing. In this paper, we investigate the synchronization of circular semi-flower automata. We first prove that every semi-flower automaton is a one-cluster automaton. Subsequently, we prove that every semi-flower automaton containing a 1-cycle is synchronizing. Further, we prove that every circular semi-flower automaton with an odd number of states containing a 2-cycle is synchronizing.
Cite
@article{arxiv.1808.01711,
title = {On the Synchronization of Circular Semi-Flower Automata},
author = {Shubh N. Singh and Ankit Raj},
journal= {arXiv preprint arXiv:1808.01711},
year = {2018}
}