Output sufficient modules for uniform decomposition of synchronous sequential circuits

Some results concerning uniform modular decomposition are presented. The primary concern is with the number of inputs which a universal module must have and also with the conditions which a module must satisfy if it is to be output sufficient. It is shown that the number of inputs required by an output sufficient module grows exponentially with the number of inputs to the sequential machines to be realized. If the special class of strongly connected modules which have a minimal number of inputs is considered, then the module is output sufficient if and only if each state of the module is output onto. This condition can be tested by a simple examination of the state table of the module. If the module has more than the minimal number of inputs, this condition is no longer necessary. A test for the output sufficiency of an arbitrary module has not yet been found.