论文标题
Muchnik悖论的各个方面
Aspects of Muchnik's paradox in restricted betting
论文作者
论文摘要
Muchnik的悖论说，枚举的博彩策略并不总是可以降低为枚举的策略，这些策略的投注仅限于回合或奇数回合。换句话说，有一个有效枚举的策略成功的结果序列X，但是没有这样的危机有效地枚举的策略。我们表征了这种$ x $的有效Hausdorff尺寸，表明它可以低至1/2但不少于。我们还表明，对于限制奇偶校验的有效枚举策略，包装尺寸低至$ \ log \ sqrt3 $。最后，在有可计算的整数值策略的情况下，我们展示了Muchnik的悖论。
Muchnik's paradox says that enumerable betting strategies are not always reducible to enumerable strategies whose bets are restricted to either even rounds or odd rounds. In other words, there are outcome sequences x where an effectively enumerable strategy succeeds, but no such parity-restricted effectively enumerable strategy does. We characterize the effective Hausdorff dimension of such $x$, showing that it can be as low as 1/2 but not less. We also show that such reals that are random with respect to parity-restricted effectively enumerable strategies with packing dimension as low as $\log\sqrt3$. Finally we exhibit Muchnik's paradox in the case of computable integer-valued strategies.
