Re:Rice’s Theorem: An interactive tutorial
by Nevermark on Friday November 25, 2022 @10:21PM
(#33749560)
Ok, but unless you stick with some fixed resource limit N forever, the problem is undecidable again.
I suppose we could pick a very large resource number N (allocatable between time and memory space?) and agree that we will create a large body of math and algorithms with the assumption of that limit, so all our theorems and programs within that finite math area are consistent.
But a great deal of math would have to be reconsidered every time N was increased.
Re:Rice’s Theorem: An interactive tutorial
by wizeman on Friday November 25, 2022 @10:40PM
(#33749663)
> Ok, but unless you stick with some fixed resource limit N forever, the problem is undecidable again.
Why do you believe that?
The existence of the cycle detection algorithms that I mentioned earlier don't assume any particular number N and yet they prove that the problem is decidable as long as N is assumed to be a finite number.
Yes! Thank you! That's exactly what I'm saying.
Now the question is: how can we do this without having to simulate the program step-by-step on all possible inputs?
Or in other words, how can we reduce the time complexity of the currently-known algorithms for solving this problem?
That's the actual interesting question!