On a Class of Threshold Transformations Having Single-cycle Attractors

The first step is to construct a class of skew-circular one-to-one threshold transformations of the Boolean n-space having single cycles of length 2n by means of [ ]representations. Then 2n-dimensional threshold transformations having single 2n-cycle attractors are constructed through expansion and neighborhood functions. The construction of ndimensional transformations having single 2n-cycle attractors is carried out through partial neighborhood functions. For the proof of attractiveness, newly-introduced extended representations and decomposition of transformations are employed.