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We present grey-box concolic testing, a novel path-based test case generation method that combines the best of both white-box and grey-box fuzzing. At a high level, our technique systematically explores execution paths of a program under test as in white-box fuzzing, a.k.a. concolic testing, while not giving up the simplicity of grey-box fuzzing: it only uses a lightweight instrumentation, and it does not rely on an SMT solver. We implemented our technique in a system called Eclipser, and compared it to the state-of-the-art grey-box fuzzers (including AFLFast, LAF-intel, Steelix, and VUzzer) as well as a symbolic executor (KLEE). In our experiments, we achieved higher code coverage and found more bugs than the other tools.