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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - I. R. Akishev
AU  - M. E. Dvorkin
TI  - On constructing minimal deterministic finite automaton recognizing a~prefix-code of a~given cardinality
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2010
SP  - 104
EP  - 116
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2010_2_a10/
LA  - ru
ID  - PDM_2010_2_a10
ER  - 
%0 Journal Article
%A I. R. Akishev
%A M. E. Dvorkin
%T On constructing minimal deterministic finite automaton recognizing a~prefix-code of a~given cardinality
%J Prikladnaâ diskretnaâ matematika
%D 2010
%P 104-116
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2010_2_a10/
%G ru
%F PDM_2010_2_a10
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/

[1] Unicode specification, http://unicode.org/

[2] Elias P., “Universal codeword sets and representations of the integers”, IEEE Trans. Inform. Theory, 21 (1975), 194–203 | DOI | MR | Zbl

[3] Golin M. J., Na H., “Optimal prefix-free codes that end in a specified pattern and similar problems: The uniform probability case (extended abstract)”, Data Compression Conference, 2001, 143–152

[4] Han Y.-S., Salomaa K., Wood D., “State complexity of prefix-free regular languages”, Proc. of the 8th Int. Workshop on Descriptional Complexity of Formal Systems, 2006, 165–176

[5] Khopkroft D. E., Motvani R., Ulman D. D., Vvedenie v teoriyu avtomatov, yazykov i vychislenii, Vilyams, M., 2002, 528 pp.

[6] Kormen T., Leizerson Ch., Rivest R., Algoritmy: postroenie i analiz, MTsNMO, BINOM, M., 2004, 960 pp.

[7] Knut D. E., Iskusstvo programmirovaniya, v. 2, Poluchislennye algoritmy, Vilyams, M., 2004, 832 pp.

[8] Bleichenbacher D., Efficiency and security of cryptosystems based on number theory, Zürich, 1996 | Zbl

[9] Cruz-Cortes N., Rodriguez-Henriquez F., Juarez-Morales R., Coello C. A., “Finding optimal addition chains using a genetic algorithm approach”, LNCS, 3801, 2005, 208–215

[10] Nedjah N., de Macedo M. L., “Finding minimal addition chains using ant colony”, IDEAL, LNCS, 3177, eds. R. Y. Zheng, R. M. Everson, Y. Hujun, 2004, 642–647

[11] Schonhage A., “A lower bound for the length of addition chains”, Theoretical Computer Science, 1:1 (1975), 1–12 | DOI | MR

[12] Flammenkamp A., Shortest addition chains, http://wwwhomes.uni-bielefeld.de/achim/addition_chain.html

[13] Downey P., Leong B., Sethi R., “Computing sequences with addition chains”, SIAM J. Computing, 10:3 (1981), 638–646 | DOI | MR | Zbl