Analysis of Linear Sequential Circuits by Confluence Sets
- 1 June 1964
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Electronic Computers
- Vol. EC-13 (3) , 226-231
- https://doi.org/10.1109/PGEC.1964.263908
Abstract
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.Keywords
This publication has 3 references indexed in Scilit:
- On periodicity of states in linear modular sequential circuits (Corresp.)IRE Transactions on Information Theory, 1959
- The Theory of Autonomous Linear Sequential NetworksIRE Transactions on Circuit Theory, 1959
- Linear Multivalued Sequential Coding NetworksIRE Transactions on Circuit Theory, 1959