A new characterization of feedforward delay-free inverses (Corresp.)

Abstract

A necessary and sufficient condition for a linear sequential circuit to possess a feedforward inverse is given for the class of linear sequential circuits that possess delay-free inverses. Unlike previous work, this condition is given in terms of the difference (state) equation matrices rather than minors of the system transfer-function matrix. The constructive proof yields the following corollary: if a linear sequential circuit requiring <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> memory elements has a feedforward delay-free inverse, then there exists at least one such inverse that requires no more than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> memory elements.