reconstruction problem; multiset; function of several arguments; commutative groupoid; semiring
Abstract :
[en] A reconstruction problem is formulated for multisets over commutative groupoids. The cards of a multiset are obtained by replacing a pair of its elements by their sum. Necessary and sufficient conditions for the reconstructibility of multisets are determined. These results find an application in a different kind of reconstruction problem for functions of several arguments and identification minors: classes of linear or affine functions over nonassociative semirings are shown to be weakly reconstructible. Moreover, affine functions of sufficiently large arity over finite fields are reconstructible.
Disciplines :
Mathematics
Author, co-author :
LEHTONEN, Erkko ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC)
Language :
English
Title :
Reconstructing multisets over commutative groupoids and affine functions over nonassociative semirings
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