Symbolic Execution/Concolic Testing on OS Kernel

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Is it possible to run Symbolic execution on Linux Kernel or parts of it? What about Concolic Testing? Thanks!

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Yes.

You can use S2E [1] to analyze binaries in-vivo (within a full software stack). Symbolic execution is S2E's default mode but you can also do concolic testing without much effort.

[1] https://s2e.systems/