Cycles in logical nets

Abstract

This paper investigates the influence of cycles in a logical net upon the complexity of its behavior. The investigation is mainly concerned with two questions: 1. 1. A logical net with a periodic input sequence produces a periodic output sequence; how is the spectrum of periodic outputs related to the level of cycle complexity?2. 2. Is there a level of complexity c (suitably defined) such that any behavior possible for a fixed logical net can be realized by a logical net constructed only of cycles of complexity c' [les] c? The first and more difficult question is fully answered only in the case of nets constructed of cycles having a feedback coefficient r = 1 (suitably defined). The second question is answered in the negative for individual cycles and it is conjectured that a similar answer holds for nets in general.