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The subject of Ap and Uap types of additional information for Bc, TxtFex, and TxtBc is covered in Jain and Sharma [85]. |
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Other approaches to additional information have been considered by Fulk [68], by Case, Kaufmann, Kinber, and Kummer [32], by Baliga and Case[1l], and by Kaufmann and Stephan [104]. |
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10-1 Consider a variant of Bexa,c-identification in which the additional information about a function f is provided as a sequence whose limiting value is an upper bound on MinProgc(f). More formally, let X range over infinite sequences of natural numbers x0, x1, x2,. . . and let  denote the limit of the sequence, if the sequence converges. |
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10.52 Definition Let a,  . |
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(a) M BEXa,c-identifies f (written:  just in case, for all X such that  ), we have  and, for  ,  . |
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(b)  |
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Show that for each a,  , Bexa,c = BEXa,c. Does a similar result hold for other paradigms in Section 10.2? |
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10-2 Complete the proof of Proposition 10.12. |
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10-3 Give a proof for Proposition 10.13. |
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It is easy to verify that  . Use Kleene's recursion theorem (Theorem 2.3) to show that  . |
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