User loginNavigation |
Halting program density?We know the density of primes tends towards 1/log(n) as n get larger. Do we know anything about the density of programs which halt? For example, take your favorite universal turing machine. Generate all programs of size 1. Record the percentage of programs that halt in less than 1 millisecond (or 10,000 head movements, or some other metric). Run the remaining programs for 10 milliseconds each, record the percentage which halt. Continue for 100, 1000, etc. milliseconds. Then repeat the procedure for all programs of length 2,3,4..N. Do we know anything about the surface just described? It surely must be monotonically increasing. Can we say anything more? Can we describe any aspect of it with numbers? This seems like it might be an easier task to undertake, compared to the corresponding question of "What's the density of provable truths in arithmetic?" Thoughts? By Greg Buchholz at 2005-03-18 16:38 | LtU Forum | previous forum topic | next forum topic | other blogs | 7300 reads
|
Browse archives
Active forum topics
|
Recent comments
9 weeks 5 days ago
14 weeks 7 hours ago
15 weeks 4 days ago
15 weeks 4 days ago
18 weeks 2 days ago
22 weeks 6 days ago
22 weeks 6 days ago
23 weeks 2 days ago
23 weeks 2 days ago
26 weeks 1 day ago