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1.  ; |
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2. WM( s ) =a L; |
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3.  . |
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The sequence s is referred to as TxtExa-locking sequence for M on L. (This is an analog of Definition 3.24 for the TxtExa paradigm.) |
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(d) For all  ,  . (Use the above locking sequence result.) Further conclude that  . |
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6-4 (J. Steel cited in Case and Smith [35]) Show  . |
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6-5 Consider the following definition. |
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6.30 Definition Let  . |
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(a) M Exta-identifies f (written:  ) just in case   . |
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(b)  . |
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Show that Exta = Ext0 = Bc. |
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6-6 Consider the following criteria of success on functions. |
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6.31 Definition (Case and Smith [35]) Let  . |
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(a) M Oexa-identifies f (written:  ) just in case there exists a nonempty finite set D such that the following hold: |
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1. for some  , j i =a f, |
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2. for all but finitely many n,  , and |
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3. for each  , there are infinitely many n such that M(f[n]) = i. |
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(b)  . |
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Thus, M Oexa identifies a function f just in case M, fed the graph of f, vacillates among a nonempty finite set D of indexes such that there is at least one a-error index for f in the set D and each index in D is conjectured infinitely often by M. Show that for each  we have that Oexm = Exm, but that  . |
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