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It seems to me that this is really a testing failure which, ironically, could be avoided by automating testing. An automated testing procedure could have ensured that every possible combination of inputs and failures was tried out.

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Not really. As Dijistra said: "Testing only proves existence of errors, not their absense."

Sure, but in this case, the testing failed to detect an error which more rigorous testing would have detected. Like I said- automated testing, trying every possible combination, would have detected the failure discussed in the article.

And how many possible combination were there to try? Even then this would cover just one class of errors.

Automated tests are great (I use them all the time). But not all situations can be covered in a test - specially when there is concurrency involved.

True, but what else can you do? Modern aircraft are too complex to fly without automation... I'm not a CS-educated programmer- are there systems for programming in a way that can somehow be proven to work for all situations? What paradigm do they use for programming at NASA?

That becomes impractical when your input space is more than a couple dozen bits, and completely impossible by the time you reach several dozen.

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