Regular Expressions for Linear Sequential Circuits

This paper considers the class of linear sequential circuits from the regular expression point of view. The circuits studied do not have special starting units which are necessary in the conventional construction of circuits from regular expressions. Since conventional regular expressions are only indirectly related to the circuit structure, a new regular language is developed. Using this language, the regular expression accepted by a linear circuit can be obtained more directly from the circuit. The regular expressions are then interpreted to provide a word description of the circuit behavior.