Analysis and synthesis of linear sequential machines.

Abstract

The material presented in this thesis can be divided into three major topics: Controllability and observability of linear sequential machines, where these principles are presented from the point of view of cyclic subspaces. Such an approach as it pertains to the direct-sum of the state space enables us to extend current results to cases other than the single input and non-derogatory state transition matrix and develop synthesis algorithms for a controllable and/or observable linear sequential machine. Minimality of a linear sequential machine, where these principles are presented from the observability point of view. This approach enables us to develop quick tests for minimality and introduce a different minimization algorithm having definite advantages when dealing with very large machines. This approach then leads us in a natural way to the consideration of minimality where the input sequence length is finite and/or the set of starting states is a subset of the set of states. Shift register synthesis of a linear sequential machine. Our first approach develops an algorithm which yields both parallel and/or serial shift register realizations by mathematically operating upon the characterizing matrices. A generalized synthesis module giving the illusion of variable hardware is presented next. Finally shift register realizations are obtained from the transfer function definition or sets of input/output sequence pairs where the length of the input sequence is finite and starting state restrictions exist.