On Monday, 29 July 2013 at 13:05:10 UTC, JS wrote:

On Monday, 29 July 2013 at 12:36:36 UTC, John Colvin wrote:On Monday, 29 July 2013 at 12:35:59 UTC, John Colvin wrote:On Monday, 29 July 2013 at 12:17:22 UTC, JS wrote:Even something like## Advertising

for(;;) { if (random() == 3) break; } is decidable(it will halt after some time).That program has a finite average runtime, but its maximumruntime is unbounded. You can't actually say it *will* halt.For any given input (in this case 0 inputs) one cannot tellwhether the program will eventually halt, therefore it isundecidable.I have formal background in CS so I might have got thattotally wrong.sorry, that should be "I have NO formal background in CS"No, again, it isn't about infinite run time. decidability != infinite run time. to simplify, let's look at the program, for(;;) if (random() == 0) break;where random() returns a random number, not necessarilyuniform, between 0 and 1.Same problem just easier to see.Since there must be a chance for 0 to occur, the program musthalt, regardless of how long it takes, even if it takes an"infinite" amount of time.That is, the run time of the program may approach infinity BUTit will halt at some point because by the definition of random,0 must occur... else it's not random.So, by the fact that random, must cover the entire range, evenif it takes it an infinitely long time(so to speak), we knowthat the program must halt. We don't care how long it will takebut just that we can decide that it will.The only way you could be right is if random wasn't random and0 was never returned... in that case the program would nothalt... BUT then we could decide that it never would halt...In both cases, we can decide the outcome... if random is knownto produce 0 then it will halt, if it can't... then it won't.But random must produce a 0 or not a 0 in an infinite amount oftime. (either 0 is in the range of random or not).That is, the halting state of the program is not random eventhough it looks like it. (again, it's not how long it takes butif we can decide the outcome... which, in this case, rests onthe decidability of random)Another way to see this, flipping a fair coin has 0 probabilityof producing an infinite series of tails.Why?After N flips, the probability of flipping exactly N tails is1/N -> 0.

`Ok, I think I get what you mean now. The 2 states of interest for`

`the halting problem are, for a give input:`

1) program *can* stop 2) program *will not* stop is that correct?