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The test case generation from design specifications is an important work in testing phase. In this paper, we use UML activity diagrams as design specifications, and present an automatic test case generation approach. The approach first randomly generates abundant test cases for a JAVA program under testing. Then, by running the program with the generated test cases, we can get the corresponding program execution traces. Last, by comparing these traces with the given activity diagram according to the specific coverage criteria, we can get a reduced test case set which meets the test adequacy criteria. The approach can also be used to check the consistency between the program execution traces and the behavior of UML activity diagrams.