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How to distinguish between a problem which is (undecidable) and which is (undecidable but partially decidable); or rather for a given problem how to say in which category it falls?

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I have seen your question I am not very sure of the answer,undecidable is sub classified as partially undecidable or semi-decidable,I don't want to confuse you with a wrong answer,Undecidable is when the Turing Machine does not halt so,semi and partial are Halting Turing Machines just for one particular case but not for the entire Grammar.Not very sure but here is what I think.Decidable is when you can make Turing Machine halt for the entire set of Languages generated by the grammar.

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