State Diagrams of T -Cyclic Autonomous Nonsingular LSC’s over $J_m $ with Multiply Irreducible Elementary Divisors
H. L. Althaus · SIAM Journal on Applied Mathematics · 1972
The linear sequential circuit (LSC) over $J_m $ was introduced by D. A. Bollman in 1963. State transitions were described in terms of the $J_m $-module M under a linear transformation. Some periodicity properties of nonsingular LSC’s over $J_m $ have since been reported (1966) but much remains to be learned about the structure of these modules. In this paper we study the cycle structure of a $J_m $-module under nonsingular linear transformation T and, for one class of LSC’s over $J_m $, present a method for determining the state diagram from the minimal polynomial of T. Two examples demonstrate the computation of state diagrams for this class of LSC’s.