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A subdirectly reducible fibered automaton 

A subdirectly reducible fibered automaton 

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Fig. 1. The fibered automaton giving binary representations
Fig. 2. A subdirectly reducible fibered automaton 
Fig. 3. A subdirectly irreducible fibered automaton 
Subdirectly irreducible fibered automata. II
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  • May 2017
An earlier paper characterized all subdirectly irreducible permutational fibered automata. This paper characterizes all subdirectly irreducible fibered automata which are not permutational. The characterization is both graphtheoretical and algebraic.
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... 4.4. Let (S, E) be a fibered automaton whose graph is a binary park with girth 4. If the labels of the cycle are e, f, e, f (see Figure 2), then (S, E) is not subdirectly irreducible. If the labels of the cycle are e, f, e, e (see Figure 3), then (S, E) is subdirectly irreducible. ...

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Fig. 2. The fibered automaton with the graph C 8 . 
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