Analysis of Linear Sequential Circuits by Confluence Sets

In this paper the group-theoretical concept of ``confluence sets'' is introduced as a valuable tool in the analysis of linear sequential circuits (LSC's). Using this concept, a scheme is formulated for producing state graphs of autonomous LSC's which, in the ``singular'' case, is superior to currently known schemes. Singular LSC's, which are of potential interest in error correction systems, are studied in detail. Properties of their state graphs are derived, culminating in a unique characterization of such graphs in terms of representative ``cycles'' and ``trees.'' Together with known results on nonsingular circuits, the results in this paper offer a description of the autonomous behavior of the general linear sequential circuit.