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Real-time embedded systems are becoming more complex to include multiple functionalities. Sharing a computing platform is a natural and effective solution to reducing the cost of those systems. However, the sharing can cause serious problems in mixed-criticality systems where applications have different levels of criticality. Certifying the mixed-criticality systems requires efficient scheduling algorithms and schedulability tests different from the ones used in single criticality systems. In this paper, we propose the first dynamic scheduling algorithm called CBEDF for certifiable mixed-criticality systems on a uniprocessor platform. We show that CBEDF dominates previously proposed algorithms OCBP. In addition, we propose a sufficient schedulability test for CBEDF. We demonstrate that the schedulability test of CBEDF out-performs that of the previously proposed algorithms by performing simulations using randomly generated instances of jobs.