SINGULAR LINEAR SEQUENTIAL MACHINES: SOME FURTHER GROUP PROPERTIES AND CANONICAL FORM REALIZATIONS,
Pierre Lavallee · Defense Technical Information Center (DTIC) · 1964
Singular autonomous linear sequential machines are analyzed following simple group properties introduced by Gill (IEEE Transactions on Electronic Computers, Vol. EC-13: 226-231, no. 3, Jun 1964, AD-607 476). It is shown that the set of junction states for the confluence sets form a group, with as normal subgroup, the sets of states on the cycle sets. The set of states mapping into the null (0) state also forms a group called the null tree group. The cycle set group and the null tree group are realized separately and the direct sum of these two groups completely characterizes the operation of the machine. The null tree is shown to be characterized by a set of m disjoint paths: to each of these paths there corresponds a shift register having as many delay elements as there are states in that path. (Author)