Geodesic
Number of labelings of definite automata graphs
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2022), pp. 71-75

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The issue concerning the number of possible labelings of directed graph's edges such that the resulting automation diagramm corresponds to a graph of a definite automaton is studied in the paper. It is proved that such a labeling is unique for a strongly-connected graph in an alphabet of two elements. In the case of an alphabet with a larger number of elements, the exponential dependence of the maximal number of labelings on the number of vertices is proved. 
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     author = {R. A. Ishchenko},
     title = {Number of labelings of definite automata graphs},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {71--75},
     publisher = {mathdoc},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2022_2_a11/}
}
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R. A. Ishchenko. Number of labelings of definite automata graphs. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2022), pp. 71-75. http://geodesic.mathdoc.fr/item/VMUMM_2022_2_a11/