The Collatz Problem,∗ the Halting Problem and Randomness
نویسنده
چکیده
A problem/conjecture is finitely refutable if verifying a finite number of instances suffices to disprove it. A systematic enumeration (of the problem’s search domain) will find a counter-example if one exists. If the search stops, the conjecture is false; if the search does not halt the conjecture is true. For a finitely refutable problem Π we can construct a program CΠ such that Π is false iff CΠ halts.
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