For an arbitrary software product, can we perform exhaustive testing to verify the correct behavior?
Question:
Answer:
Certainly, I don't see why not. You would want to do this to ensure the product meets the design specifications.
When you say arbitrary i am assuming you don't know the functionality of the product or limited knowledge on the functionality.
Without understanding the functionality of the software product, an exhaustive testing will only capture superficial defects like i/o, validation etc. You'll never be able to capture the functional defects.
You need to first define "correct behavior"
To the extent you codify what constitutes "correct behavior" you can verify it.
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