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Wafer-level testing (wafer sort) is used in the semiconductor industry to reduce packaging and test cost. However, a large number of wafer-probe contacts lead to higher yield loss. Therefore, it is desirable that the number of chip pins contacted by tester channels during wafer sort be kept small to reduce the yield loss resulting from improper contacts. Since test time and the number of contacted chip pins are major practical constraints for wafer sort, not all scan-based digital tests can be applied to the die under test. We propose an optimization framework based on mathematical programming (integer linear programming, nonlinear programming, and geometric programming) and fast heuristic methods. This framework addresses test-access mechanism (TAM) optimization and test-length selection for wafer-level testing of core-based digital system-on-chips (SoCs). The objective here is to design a TAM architecture and determine test lengths for the embedded cores such that the overall SoC defect-screening probability at wafer sort is maximized. Defect probabilities for the embedded cores, obtained using statistical yield modeling, are incorporated in the optimization framework. Simulation results are presented for five of the ITC'02 SoC Test benchmarks.