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Using the concept of discrete noiseless channels, it was shown by Shannon inA Mathematical Theory of Communication that the ultimate performance of anencoder for a constrained system is limited by the combinatorial capacity ofthe system if the constraints define a regular language. In the present work,it is shown that this is not an inherent property of regularity but holds ingeneral. To show this, constrained systems are described by generatingfunctions and random walks on trees.

Maximum Entropy Rate of Markov Sources for Systems With Non-regular Constraints