A new method for describing and analyzing finite determined automata by Walsh functions

Discrete event systems are often modelled by finite determined automata (FDA). A new approach for modelling is proposed, which provides a linear discrete event system: X_k+1 = A · x_k- An algorithm is given to calculate the system matrix A without solving any system of linear equations (SLE). In analogy to the meaning of eigenvalues of a discrete time system, a connection between the eigenvalues and the cycles of the FDA exists. It is shown. though, that the cycles of the FDA can found without computing the eigenvalues. The new method can also be used to describe and analyze Petri nets. Deadlocks can be found easily, because they are cycles of length one. The method is also useful for identifying isomorphisms between different Petri nets.