Symmetric Function Essential Variable Subfunction Identification Minor Essential Arity Gap Gap Index Separable Set
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Journal of Computing, Vol. 6, No 4, (2012), 419p-436p
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.