# Unique decipherability in the additive monoid of sets of numbers

RAIRO - Theoretical Informatics and Applications (2011)

- Volume: 45, Issue: 2, page 225-234
- ISSN: 0988-3754

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topSaarela, Aleksi. "Unique decipherability in the additive monoid of sets of numbers." RAIRO - Theoretical Informatics and Applications 45.2 (2011): 225-234. <http://eudml.org/doc/276337>.

@article{Saarela2011,

abstract = {
Sets of integers form a monoid, where the product of two sets A
and B is defined as the set containing a+b for all $a\in A$ and
$b\in B$. We give a characterization of when a family of finite
sets is a code in this monoid, that is when the sets do not satisfy
any nontrivial relation. We also extend this result for some
infinite sets, including all infinite rational sets.
},

author = {Saarela, Aleksi},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Unique decipherability; rational set; sumset; unique decipherability},

language = {eng},

month = {6},

number = {2},

pages = {225-234},

publisher = {EDP Sciences},

title = {Unique decipherability in the additive monoid of sets of numbers},

url = {http://eudml.org/doc/276337},

volume = {45},

year = {2011},

}

TY - JOUR

AU - Saarela, Aleksi

TI - Unique decipherability in the additive monoid of sets of numbers

JO - RAIRO - Theoretical Informatics and Applications

DA - 2011/6//

PB - EDP Sciences

VL - 45

IS - 2

SP - 225

EP - 234

AB -
Sets of integers form a monoid, where the product of two sets A
and B is defined as the set containing a+b for all $a\in A$ and
$b\in B$. We give a characterization of when a family of finite
sets is a code in this monoid, that is when the sets do not satisfy
any nontrivial relation. We also extend this result for some
infinite sets, including all infinite rational sets.

LA - eng

KW - Unique decipherability; rational set; sumset; unique decipherability

UR - http://eudml.org/doc/276337

ER -

## References

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- Ch. Choffrut and J. Karhumäki, Unique decipherability in the monoid of languages: an application of rational relations, in Proceedings of the Fourth International Computer Science Symposium in Russia (2009) 71–79. Zbl1248.94044
- R. Gilmer, Commutative Semigroup Rings. University of Chicago Press (1984). Zbl0566.20050
- J.-Y. Kao, J. Shallit and Z. Xu, The frobenius problem in a free monoid, in Proceedings of the 25th International Symposium on Theoretical Aspects of Computer Science (2008) 421–432. Zbl1259.68166
- J. Karhumäki and L.P. Lisovik, The equivalence problem of finite substitutions on $a{b}^{*}c$, with applications. Int. J. Found. Comput. Sci.14 (2003) 699–710. Zbl1101.68660
- M. Kunc, The power of commuting with finite sets of words. Theor. Comput. Syst.40 (2007) 521–551. Zbl1121.68065
- D. Perrin, Codes conjugués. Inform. Control. 20 (1972) 222–231. Zbl0254.94015
- J.L. Ramírez Alfonsín, The Diophantine Frobenius Problem. Oxford University Press (2005). Zbl1134.11012

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