Geodesic
On constructing minimal deterministic finite automaton recognizing a~prefix-code of given cardinality
Prikladnaâ diskretnaâ matematika, no. 12 (2010), pp. 92-94

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The article considers the problem of constructing minimal deterministic finite automaton recognizing a prefix-code of a given cardinality over the alphabet $\{0,1\}$. The considered problem is proved to be equivalent to the problem of finding the shortest addition-chain ending with a given number. Several interesting properties of the desired minimal finite automaton are proved, and the identical problem concerning Moore automata is discussed. 
@article{PDM_2010_12_a46,
     author = {I. R. Akishev and M. E. Dvorkin},
     title = {On constructing minimal deterministic finite automaton recognizing a~prefix-code of given cardinality},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {92--94},
     publisher = {mathdoc},
     number = {12},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2010_12_a46/}
}
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I. R. Akishev; M. E. Dvorkin. On constructing minimal deterministic finite automaton recognizing a~prefix-code of given cardinality. Prikladnaâ diskretnaâ matematika, no. 12 (2010), pp. 92-94. http://geodesic.mathdoc.fr/item/PDM_2010_12_a46/