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You can not reconstruct the specification from just the code. For one thing, you don't know whether the code is correct or not. For another, there are multiple possible specifications that are all co …

In principle it is possible to express this condition using something like Hoare logic, but it's not clear it will be very useful or practical to do so. Consider a function $f$ in your program, with …

The statespace explosion problem. More specifically, software often uses unbounded loops, pointers into complex data structures on the heap, and dynamic allocation. Each of these can cause rapid sta …

Generally you have: Some boolean variables that collectively represent the current state, say $s,t,u$. Some boolean variables that collectively represents the inputs, say $i,j,k$. For instance, you …

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 …

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 …

"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 …

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 …

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 …

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 …

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 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 …

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 …

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 …

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 …