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Download fileFactorization in formal languages
conference contribution
posted on 2015-09-25, 08:48 authored by Paul Bell, Daniel Reidenbach, J.O. ShallitWe consider several language-theoretic aspects of unique factorization in formal languages. We reprove the familiar fact that the set uf(L) of words having unique factorization into elements of L is regular
if L is regular, and from this deduce an quadratic upper and lower bound on the length of the shortest word not in uf(L). We observe that uf(L) need not be context-free if L is context-free. Next, we consider some variations on unique factorization. We de ne a notion of \semi-unique" factorization, where every factorization has the same number of terms, and show that, if L is regular or even nite, the set of words having such a factorization need not be context-free. Finally, we consider additional variations, such as unique factorization \up to permutation" and \up to subset". Although all these variations have
been considered before, it appears that the languages of words having these properties have not been positioned in the Chomsky hierarchy up to now. We also consider the length of the shortest word not having the
desired property.
History
School
- Science
Department
- Computer Science
Published in
Developments in Language TheoryVolume
9168Issue
1Pages
97 - 107 (11)Citation
BELL, P.C., REIDENBACH, D. and SHALLIT, J.O., 2015. Factorization in formal languages. IN: Potapov, I (ed). 19th International Conference on Developments in Language Theory, Liverpool, UK, 27-30 July, pp. 97 - 107Publisher
© Springer International PublishingVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2015Notes
The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-21500-6ISBN
978-3-319-21500-6;978-3-319-21499-3Publisher version
Book series
Lecture Notes in Computer Science;9168Language
- en