This paper discusses the fundamental combinatorial question of whether or not, for a given string α, there exists a morphism σ such that σ is unambiguous with respect to α, i.e. there exists no other morphism τ satisfying τ(α) = σ(α). While Freydenberger et al. [Int. J. Found. Comput. Sci. 17 (2006) 601-628] characterise those strings for which there exists an unambiguous nonerasing morphism σ, little is known about the unambiguity of erasing morphisms, i.e. morphisms that map symbols onto the empty string. The present paper demonstrates that, in contrast to the main result by Freydenberger et al., the existence of an unambiguous erasing morphism for a given string can essentially depend on the size of the target alphabet of the morphism. In addition to this, those strings for which there exists an erasing morphism over an infinite target alphabet are characterised, complexity issues are discussed and some sufficient conditions for the (non-)existence of unambiguous erasing morphisms are given.
Mots-clés : combinatorics on words, morphisms in free monoids, unambiguity, complexity
@article{ITA_2010__44_2_193_0,
author = {Schneider, Johannes C.},
title = {Unambiguous erasing morphisms in free monoids},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {193--208},
publisher = {EDP-Sciences},
volume = {44},
number = {2},
year = {2010},
doi = {10.1051/ita/2009020},
mrnumber = {2674540},
zbl = {1203.68132},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ita/2009020/}
}
TY - JOUR AU - Schneider, Johannes C. TI - Unambiguous erasing morphisms in free monoids JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2010 SP - 193 EP - 208 VL - 44 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita/2009020/ DO - 10.1051/ita/2009020 LA - en ID - ITA_2010__44_2_193_0 ER -
%0 Journal Article %A Schneider, Johannes C. %T Unambiguous erasing morphisms in free monoids %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2010 %P 193-208 %V 44 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita/2009020/ %R 10.1051/ita/2009020 %G en %F ITA_2010__44_2_193_0
Schneider, Johannes C. Unambiguous erasing morphisms in free monoids. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) no. 2, pp. 193-208. doi : 10.1051/ita/2009020. http://www.numdam.org/articles/10.1051/ita/2009020/
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