Sequential machines realized by group representations

AbstractWell-known results yield a decomposition of a sequential machine into permutation and reset machines. This paper presents a methodology for the realization of the permutation machines; this methodology involves group representation theory. In the worst case, any permutation machine can be realized by a set of matrices multiplied modulo three. Bounds on the dimensions of these matrices are given. It is further shown that realization can always be performed over roots of unity, and that appropriate fields for realization can be found by solving a very simple equation