Pseudo-Boolean Matrix Techniques for State Minimisation of Finite State Machine Realisations of DSP Systems.

Abstract

It is explored the mathematical basis of state reduction techniques, which have been developed in the design of Minimum Complexity Finite State Machines. The technique is based upon using first or second order Markovian Models and Pseudo-Boolean Matrices, to minimise the requisite number of states to implement IIR and FIR Digital Filters as well as DFT algorithms. The Boolean and the double BooleanDifference factors are then calculated to provide a measure of dependancy of state transitions for different arities. Rules are beinbeing developed for the connection of Pseudo-Boolean Matrices for different nodes and loops.