Inverse problems in coding, automata, and continuous systems

The investigation presents explicit interconnections between inverse problems in the theories of convolutional codes, automata, and continuous time linear dynamical systems. In a code-generating, or transfer function, matrix framework, necessary and sufficient conditions are given for a feedforward linear sequential circuit to have a feedforward inverse, either instantaneous or with delay. In the corresponding state-oriented realization, techniques which have been applied to construct inverses for continuous time linear dynamical systems are used to outline the construction of inverse automata. Finally, the feedforward inverse results are applied to continuous time systems. Relationships between the results are discussed.