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Unique decipherability in the additive monoid of sets of numbers

Published online by Cambridge University Press:  13 May 2011

Aleksi Saarela
Aleksi Saarela*
Affiliation:
Department of Mathematics and Turku Centre for Computer Science TUCS, University of Turku, 20014 Turku, Finland; [email protected]
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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.

Keywords

Unique decipherabilityrational setsumset
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 45 , Issue 2 , April 2011 , pp. 225 - 234
Copyright
© EDP Sciences, 2011

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