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Title: Finite Symmetric Functions with Non-Trivial Arity Gap
Authors: Shtrakov, Slavcho
Koppitz, Jörg
Keywords: Symmetric Function
Essential Variable
Identification Minor
Essential Arity Gap
Gap Index
Separable Set
Issue Date: 2012
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Journal of Computing, Vol. 6, No 4, (2012), 419p-436p
Abstract: Given an n-ary k-valued function f, gap(f) denotes the essential arity gap of f which is the minimal number of essential variables in f which become fictive when identifying any two distinct essential variables in f. In the present paper we study the properties of the symmetric function with non-trivial arity gap (2 ≤ gap(f)). We prove several results concerning decomposition of the symmetric functions with non-trivial arity gap with its minors or subfunctions. We show that all non-empty sets of essential variables in symmetric functions with non-trivial arity gap are separable. ACM Computing Classification System (1998): G.2.0.
ISSN: 1312-6555
Appears in Collections:Volume 6 Number 4

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