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Rice’s theorem says no such thing. Rice’s theorem tells you you can’t necessarily prove you’ve built a flawless system, not that you can’t build a flawless syst
by legalcorrection 4y ago
Rice’s theorem says no such thing. Rice’s theorem tells you you can’t necessarily prove you’ve built a flawless system, not that you can’t build a flawless system. You can build a perfect program even if you can’t necessarily then know you have.
Perhaps you interpreted my post to suggest that you could build a machine that verifies that any arbitrary software run on it never enters an invalid state? If so, I agree, that is not possible. I made a minor edit to make it clear what I’m talking about.
- mkleczek 4y ago> Rice’s theorem tells you you can’t prove you’ve built a flawless system, not that you can’t build a flawless system. If you think about it - it is the same: how do you know the system you just built is flawless?
- ncmncm 4y agoBecause you built it in a series of steps, exactly zero of which introduced any undecidability.
- mkleczek 4y agoSee above - there is no reliable procedure (algorithm) that would allow you to build a TM with arbitrary properties (ie. implementing arbitrary requirements).
- SAI_Peregrinus 4y agoPrograms don't have to have Turing-complete behavior. Compilers do, but not every program needs to implement uncomputable behavior on its inputs.
- mkleczek 4y agoActually it's the other way around: In reality most interesting programs accept Turing complete languages - albeit not formally specified :)
- legalcorrection 4y agoYou don't, but it's still flawless. My point was that it was theoretically, not practically possible. So your retort that it's not practically possible is kind of missing the point.
- mkleczek 4y agoMy point is that it is _theoretically_ not possible: there is no algorithm that would allow you to build a TM implementing arbitrary requirements. You have to use ad-hoc methods but then it is not possible to know your ad-hoc method is correct! So by "flawless" you can only mean "having some property but we cannot say what property it is". Edit: added "flawless" definition
- legalcorrection 4y agoI'm not sure you're getting this. Let's say you want to build a video chat application with all of the same features as Zoom and not a single bug. That is, in fact, possible. Nothing about Rice's Theorem says you can't build a program without bugs. You can build a flawless video chat application. You won't, but you can. How? Very easy. Every time you're about to write code with a bug, don't. Write that same code but without the bug.
- mkleczek 4y ago> Every time you're about to write code with a bug, don't. Write that same code but without the bug. This procedure (algorithm) is ill-defined (is not realisable by a TM) as it would require verifying two things: a) the code you are about to write has a bug (ie. has a specific property) b) the code you wrote does not have a bug (ie. has a specific property) Rice's theorem says both are impossible.
- legalcorrection 4y agoMaybe moving to a specific instance of Rice's theorem is clearer. My point is that while he can't solve the halting problem—i.e. he can't reliably determine whether any arbitrary program will halt—an infallible programmer can reliably write his own programs such that they always halt. So, to go back to the original point, you can't reliably determine the correctness of every possible program. But you could, if you were not prone to error like all humans, always write your own programs such that they are always correct.