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Due to the increasing test data volume needed to test corebased System-on-Chip, several test scheduling techniques minimizing the test application time have been proposed. In contrast to approaches where a fixed test set for each core is assumed, we explore the possibility to use overlapping test patterns from the tests in the system. The overlapping tests serves as alternatives to the original dedicated test for the cores and, if selected, they are transported to the cores in a broadcasted manner so that several cores are tested concurrently. We have made use of a Constraint Logic Programming technique to select suitable tests for each core in the system and schedule the selected tests such that the test application time is minimized while designer-specified hardware constraints are satisfied. The experimental results indicate that we can on average reduce the test application time with 23%.