In a previous paper [L. Giambruno and S. Mantaci, Theoret. Comput. Sci. 411 (2010) 1785-1792] a bideterministic transducer is defined for the bidirectional deciphering of words by the method introduced by Girod [IEEE Commun. Lett. 3 (1999) 245-247]. Such a method is defined using prefix codes. Moreover a coding method, inspired by the Girod's one, is introduced, and a transducer that allows both right-to-left and left-to-right decoding by this method is defined. It is proved also that this transducer is minimal. Here we consider the number of states of such a transducer, related to some features of the considered prefix code X. We find some bounds of such a number of states in relation with different notions of “size” of X. In particular, we give an exact formula for the number of states of transducers associated to maximal prefix codes. We moreover consider two special cases of codes: maximal uniform codes and a class of codes, that we name string-codes. We show that they represent, for maximal codes, the extreme cases with regard to the number of states in terms of different sizes. Moreover we prove that prefix codes corresponding to isomorphic trees have transducers that are isomorphic as unlabeled graphs.
Mots-clés : variable length codes, prefix codes, bilateral decoding, transducers
@article{ITA_2012__46_2_315_0,
author = {Giambruno, Laura and Mantaci, Sabrina},
title = {On the size of transducers for bidirectional decoding of prefix codes},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {315--328},
publisher = {EDP-Sciences},
volume = {46},
number = {2},
year = {2012},
doi = {10.1051/ita/2012006},
mrnumber = {2931251},
zbl = {1278.94038},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ita/2012006/}
}
TY - JOUR AU - Giambruno, Laura AU - Mantaci, Sabrina TI - On the size of transducers for bidirectional decoding of prefix codes JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2012 SP - 315 EP - 328 VL - 46 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita/2012006/ DO - 10.1051/ita/2012006 LA - en ID - ITA_2012__46_2_315_0 ER -
%0 Journal Article %A Giambruno, Laura %A Mantaci, Sabrina %T On the size of transducers for bidirectional decoding of prefix codes %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2012 %P 315-328 %V 46 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita/2012006/ %R 10.1051/ita/2012006 %G en %F ITA_2012__46_2_315_0
Giambruno, Laura; Mantaci, Sabrina. On the size of transducers for bidirectional decoding of prefix codes. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 2, pp. 315-328. doi : 10.1051/ita/2012006. http://archive.numdam.org/articles/10.1051/ita/2012006/
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