Can the following two statistics be bounded:the proportion of halting programs vs non-halting programsthe proportion of decidable vs undecidable languagesFor example, can we say that one class is much larger than the other, almost all problems are such and such, or both are similar in size?By Chaitin's argument on the Omega number, we know that the halting probability is undecidable, so it is difficult to obtain an exact statistic on the number (if not impossible). However, Omega numbers have been computed for specific universal machines for prefix-free programs using probability measures decreasing in length (cf. Calude et al.). So are there known valid statements about these proportions? My intuition (following the argument of the scarcity of life in the universe) would lead me to believe that there are much more undecidable languages than decidable ones. But it is only an intuition that is not backed.
The proportion of halting programs vs non-halting programs, of decidable programs vs undecidable languages
undecidability;halting problem