Subfunction relations defined by the clones containing all unary operations
Abstract
Description
For a class C of operations on a nonempty base set A, an operation f is called a C-subfunction of an operation g, if f = g(h_1, ..., h_n), where all the inner functions h_i are members of C. Two operations are C-equivalent if they are C-subfunctions of each other. The C-subfunction relation is a quasiorder if and only if the defining class C is a clone. The C-subfunction relations defined by clones that contain all unary operations on a finite base set are examined. For each such clone it is determined whether the corresponding partial order satisfies the descending chain condition and whether it contains infinite antichains.
15 pages
15 pages