K. Tadaki, A generalization of Chaitin's halting probability# and halting selfsimilar sets, Hokkaido Math. J., Vol. 32 (2002), 219-253. Home/Search Document Not in Database Summary Related Articles Check |
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Effective Strong Dimension, Algorithmic.. - Athreya.. (2004) (Correct)
....(6.1) The following theorem is a dual of (6.2) that yields a dual of (6.1) as a corollary. 1] Proof. This proof is analogous to the one for the dual statement (6.2) given in [21] Corollary 6.2. For all S . By Corollary 6. 2, the upper algorithmic dimension defined by Tadaki [41] is precisely the constructive strong dimension. The rate at which a gambler can increase its capital when betting in a given situation is a fundamental concern of classical and algorithmic information and computational learning theories. In the setting of constructive gamblers, the following ....
....with dim(R) Dim(R) H( # #) Note that Corollary 6.15 strengthens Theorem 7.6 of [21] because the convergence of H n ( #) is a weaker hypothesis than the convergence of #. 22 Generalizing the construction of Chaitin s random real number# [6] Mayordomo [27] and, independently, Tadaki [41] defined for each s 1 # , the real number A = # # 1 # and U(#) where U is a universal self delimiting Turing machine. Given (6.1) and Corollary 6.2 above, the following fact is implicit in Tadaki s paper. Theorem 6.16. Tadaki [41] For each s 1 # , the (binary ....
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K. Tadaki. A generalization of Chaitin's halting probability # and halting self-similar sets. Hokkaido Mathematical Journal, 31:219--253, 2002.
Some Recent Progress in Algorithmic Randomness - Downey (Correct)
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K. Tadaki, A generalization of Chaitin's halting probability# and halting selfsimilar sets, Hokkaido Math. J., Vol. 32 (2002), 219-253.
Effective Fractal Dimensions - Lutz (Correct)
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K. Tadaki. A generalization of Chaitin's halting probability ! and halting self-similar sets. Hokkaido Mathematical Journal, 31:219-253, 2002.
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