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Video processing on programmable platforms offers significant advantages over dedicated hardware such as shorter development cycles, flexibility, and upgradability, among others. Although the emergence of powerful media processors is making video processing on programmable platforms closer to reality, practical media-processor-based systems benefit from complexity-scalable video processing algorithms that can trade off video quality against computation while ensuring real-time performance. We develop complexity-scalable MPEG-2 video decoding algorithms with both SNR quality degradation and decoding resolution reduction. We improve the decoder's complexity-quality performance by employing signal-adaptive processing in decoding blocks and picture-type-dependent processing with unequal computation resource allocation to exploit each picture type's varying impact on the overall video quality. Realizing that software video decoding operates in a dynamic environment where both the actual computation (depending on video data) and computation allocation (depending on other functions running simultaneously) vary, we develop dynamic complexity regulation techniques to ensure that the decoding complexity stays within allocation. Simulation results on complexity-scalable MPEG-2 video decoding and dynamic complexity regulation on media processors are presented.