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As Wikipedia says, not every property is a safety property or a liveness property (consider "a occurs exactly once") The parenthetical gives an example of a property that is not a safety property, n …

This is likely to be a very hard problem, so hard that I don't think you should expect a useful solution that can handle all possible regexes. The extended regular expressions supported by Python's re …

There is no proof that it is impossible, but it is believed that it's unlikely to be possible, because if you could convert every circuit with NAND gates to 2CNF, you would have a proof that P = …

Yes. One can find invariants in any program. The notion is well-defined and meaningful in any program (whether it is useful in practice is a different question). Normally identifying invariants is m …

The idea is that $\delta_j^{(i)}=1$ means that the input to the ReLU was negative (so its output is zero), and $\delta_j^{(i)}=0$ means that the input to the ReLU was positive (so its output is positi …

It is helpful to know basic mathematics and logic. But I would suggest that you go ahead and study software verification now, and learn additional logical background as needed. There is an unending …

If you want a guarantee, then yes, verification is the only approach. That's pretty much the definition of what verification means. If you want a heuristic check, there are a number of testing metho …

The way to incorporate it in a model depends on (a) what aspects of system behavior you want the model to capture, (b) what properties you want to verify of the system, and (c) what kind of expressivi …

I recommend that you translate while(c) b to def myWhile() = if (c) then (b ; myWhile()) myWhile() With this translation, the precondition of myWhile is the loop invariant of the original while …

Formal verification often involves at least three steps: Make a formal model of the real-world system. (The formal model might be a state-transition graph or automaton, for example.) Write down a …

It feels to me like this has already been explained before (1, 2). To prove that an automaton is correct, you first must define what correctness means to you. Usually that is done by writing a speci …

"contents are equal" implies that their lengths are equal, so you don't need double induction. Instead, try single induction. A straightforward induction argument on the length of the list should su …

First off, you're absolutely right: you're on to a real concern. Formal verification transfers the problem of confidence in program correctness to the problem of confidence in specification correctne …

Tests can be written based on either a formal spec or an informal spec. Verification always requires a formal specification. Formal verification might be manual or automated, or some combination of …

Which should you use? Neither. Personally, I think the words "taintness" and "taintedness" both look awkward. I would recommend rephrasing the sentence to avoid using either of those words. Inste …