Decidable implies that the problem can be given a precise answer for each instance of this problem. To reach a precise answer for an instance of the problem a known and proven method is required. Close or probably is not a decidable answer.
If you can prove that there exit some instances of the problem that cannot reach a conclusive and precise answer the problem is not decidable.
Knowledge and learning, in my opinion, has a lot to do with problems that need a good enough answer.
Say you just want to know if there is a high risk of infinite loops the halting-problem comes in another light. It is always not decidable though.
Learning means open for added experience in some sort. So there should often be room for more experience that hopefully leads to more exact judgments/answers. More experience can come with a 'training-cost'. By knowing how precise answer is needed this cost can be smaller.
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Monday, December 8, 2008
Something about decidable
Sunday, December 7, 2008
StubPass Tickets
Saturday, December 6, 2008
Halting problem and Artificial Intelligence
So we all know that solving the Halting problem is impossible (i.e. it's not decidable). It's also impossible to create a program that is capable of analyzing other computer programs because this problem is equivalent to the Halting problem. (i.e. The program being analyzed could have an infinite loop and there is no way to detect this infinite loop because of the Halting problem).
If we cannot create a program that can analyze other programs then we cannot create a machine that is capable of learning from other machines. In order for a machine to learn from the behavior of other machines it has to be programmed in such a way so that it could analyze other programs and we already said that this is impossible.
One fundamental property of our mind is its ability to learn by, for example, analyzing the behavior of other human beings.
If we cannot create a machine that is capable of learning then would not that mean that there is little hope for duplicating our minds through technology?