Analysis of Bilateral Iterative Networks

In the usual iterative switching circuit, which may be considered the space analog of a synchronous sequential transducer, the output of any cell is dependent only upon the inputs of the cells to its left. This paper describes a more general type of one-dimensional iterative network in which the output of each cell may be a function of the inputs of all the cells in the network, both to the left and to the right of the given cell. Starting from a table of combinations which specifies the behavior of an individual cell, a means of describing the steady-state behavior of the entire network is developed. This description is readily reduced to a fairly simple canonic form, so that equivalent networks can be recognized. Certain types of redundancy which do not occur in an ordinary iterative or sequential network are discussed, and a means of detecting these redundancies is described. Examples are presented which indicate that the process of removing redundancies is more complex than the corresponding process in the sequential case. Finally, one method of synthesizing a stable bilateral iterative network is described, and some of the problems of transient behavior are indicated.