A systematic study for representing a finite state machine as a polynomial over Galois Field is presented. A Discrete Fourier Transform method is developed for computing the coefficients of polynomials. The representation of the machines which inputs and outputs possess different word lengths is presented. The cyclic subgroup property of the polynomial coefficients is revealed. This property considerably reduces the amount of computation. The conversion between one and multiple variable machines is discussed. The Ring-Sum representation and Fast Reed-Muller Transformation are also discussed.
Galois Field Representation of Finite State Machines
Footprints in Cambridge and Aviation Industries of China ; Chapter : 6 ; 58-87
2021-09-20
30 pages
Article/Chapter (Book)
Electronic Resource
English
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