Some New Group Theoretic Properties of Singular Linear Sequential Machines

In this short paper it is shown how some simple concepts of group theory are used in the analysis of singular linear sequential machines: specifically it is shown that a set of states called the junction states form a group and more important a subgroup of the group (the set of junction states which belongs to the set of states mapping into the 0 state after 1 unit of time) plays a fundamental role in its relation to synthesis.