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The Conti-Boston factorization theorem (CBFT) for linear tail-biting trellisrealizations is extended to group realizations with a new and simpler proof,based on a controller granule decomposition of the behavior and knowncontrollability results for group realizations. Further controllability resultsare given; e.g., a trellis realization is controllable if and only if its top(controllability) granule is trivial.

Unique Factorization and Controllability of Tail-Biting Trellis Realizations via Controller Granule Decompositions