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Linux's Staging Area To Now Reject LLM-Generated Patches, Except For Real Security Fixes
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We're talking about different kind of proofs.
Proving a program is correct requires a formal specification and a formal verification with mathematics and/or formal methods. ie proving the behavior and result perfectly match specification for all possible inputs.
A test only proves that a program 1) returns the expected output for a specific input, or limited set of inputs, and 2) appears to behave correctly, ie there may be undefined behaviour but they don't cause an immediate crash.