Some New Results on the Convergence, Oscillation, and Reliability of Polyfunctional Nets

The properties of m×1 homogeneous polyfunctional nets under iteration (a growth process in which each element is replaced by a copy of the original net) are explored in considerable detail. Theorems are proved which relate the sequence of sets of output functions of a net to its structure as well as to the set of functions performed by the elements of the net. A complete characterization with respect to convergence of the 2×1 bordered net is given. Many new results on the oscillation properties of these nets are obtained, including methods for constructing nets which oscillate with prescribed period. The reliability properties of nets whose initial function assignments contain sum, product, and majority functions are studied. For the class of m×1 bordered nets (nets only slightly less general than the m×1 nets) it is shown that arbitrary reliability for these functions can be obtained under extremely broad conditions.