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The complexity of linear, fixed-point arithmetic, digital controllers is investigated from a Kolmogorov-Chaitin perspective. Based on the idea of Kolmogorov-Chaitin complexity, practical measures of complexity are developed for both state-space realizations, and for parallel and cascade realizations. The complexity of solutions to a restricted complexity controller benchmark problem is investigated using this measure. The results show that, from a Kolmogorov-Chaitin viewpoint, higher-order controllers with a shorter word-length may have a lower complexity but a better performance than lower-order controllers with longer word-length.