# Unambiguous erasing morphisms in free monoids

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 44, Issue: 2, page 193-208
- ISSN: 0988-3754

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topSchneider, Johannes C.. "Unambiguous erasing morphisms in free monoids." RAIRO - Theoretical Informatics and Applications 44.2 (2010): 193-208. <http://eudml.org/doc/250782>.

@article{Schneider2010,

abstract = {
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.
},

author = {Schneider, Johannes C.},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Combinatorics on words; morphisms in free monoids;
unambiguity; complexity; combinatorics on words; unambiguity},

language = {eng},

month = {5},

number = {2},

pages = {193-208},

publisher = {EDP Sciences},

title = {Unambiguous erasing morphisms in free monoids},

url = {http://eudml.org/doc/250782},

volume = {44},

year = {2010},

}

TY - JOUR

AU - Schneider, Johannes C.

TI - Unambiguous erasing morphisms in free monoids

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/5//

PB - EDP Sciences

VL - 44

IS - 2

SP - 193

EP - 208

AB -
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.

LA - eng

KW - Combinatorics on words; morphisms in free monoids;
unambiguity; complexity; combinatorics on words; unambiguity

UR - http://eudml.org/doc/250782

ER -

## References

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- D.D. Freydenberger and D. Reidenbach, The unambiguity of segmented morphisms. In Proc. 11th International Conference on Developments in Language Theory, DLT 2007. Lect. Notes Comput. Sci. (2007) 181–192. Zbl1202.68225
- D.D. Freydenberger, D. Reidenbach and J.C. Schneider, Unambiguous morphic images of strings. Int. J. Found. Comput. Sci.17 (2006) 601–628. Zbl1110.68119
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- A. Mateescu and A. Salomaa, Patterns, edited by G. Rozenberg and A. Salomaa, Handbook of Formal Languages1, Chap. 4.6. Springer (1997) 230–242.
- D. Reidenbach, A non-learnable class of E-pattern languages. Theoret. Comput. Sci.350 (2006) 91–102. Zbl1086.68116
- D. Reidenbach, Discontinuities in pattern inference. Theoret. Comput. Sci.397 (2008) 166–193. Zbl1145.68027
- D. Reidenbach and J.C. Schneider, Morphically primitive words, in Proc. 6th International Conference on Words, WORDS 2007 (2007) 262–272. Zbl1166.68036
- J.C. Schneider, Unambiguous erasing morphisms in free monoids, in Proc. SOFSEM 2009: Theorie and Practice of Computer Science. Lect. Notes Comput. Sci.5404 (2009) 473–484. Zbl1206.68198

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