Geodesic
On constructing minimal deterministic finite automaton recognizing a~prefix-code of a~given cardinality
Prikladnaâ diskretnaâ matematika, no. 2 (2010), pp. 104-116

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The article considers 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.
Keywords: prefix code, finite-state machine, Moore automaton, addition chain. 
@article{PDM_2010_2_a10,
     author = {I. R. Akishev and M. E. Dvorkin},
     title = {On constructing minimal deterministic finite automaton recognizing a~prefix-code of a~given cardinality},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {104--116},
     publisher = {mathdoc},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2010_2_a10/}
}
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I. R. Akishev; M. E. Dvorkin. On constructing minimal deterministic finite automaton recognizing a~prefix-code of a~given cardinality. Prikladnaâ diskretnaâ matematika, no. 2 (2010), pp. 104-116. http://geodesic.mathdoc.fr/item/PDM_2010_2_a10/