Finite group homomorphic sequential systems.

Abstract

A class of finite-state sequential systems evolving in groups is considered. It represents a broader class of input-output relations than those found in linear system theory. The concepts of controllability, observability, minimality, realizability, and the isomorphism of minimal realizations are developed. Results that are analogous to, but differ in essential details from, those of linear system theory are derived. Algorithmic design and algebraic decoding may benefit from these results.