Modeling and analyzing finite state automata in the finite field F2

A method for determining multilinear state space models for general finite state automata is presented. The obtained model resides on F2, the finite field of characteristic 2 with the operations addition and multiplication, both carried out modulo 2. It is functionally complete in the sense that it is capable of describing all finite state automata, including non-deterministic and partially defined automata. For those cases in which the model over F2 is linear, means for a complete analysis of the cyclic behavior of these automata are recalled. With respect to these linear models, the cyclic structure of the state space is shown to be determined only by the periods of the elementary divisor polynomials of the system dynamics. An example illustrates the analysis procedure.