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Discrete-Time Systems with the Decomposition Property

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2 Author(s)

The decomposition property, a necessary condition for linearity, is defined for discrete-time systems. N-state machines with this property have finite memory μ≤N−1. Linear and autonomous systems are important classes of systems with decomposition. Several representations of systems with decomposition are given and a general form of the discrete-time state equations for a finite-memory system with decomposition is derived. An algorithm is developed by which an arbitrary complete-sequential machine may be tested for decomposition.

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Computers, IEEE Transactions on  (Volume:C-19 ,  Issue: 5 )