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Weak String Erasure: Difference between revisions
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** <math>A_\mathcal{I}</math> denotes the sub-string of <math>A_1^n</math> whose bit are in <math>\mathcal{I}</math>. | ** <math>A_\mathcal{I}</math> denotes the sub-string of <math>A_1^n</math> whose bit are in <math>\mathcal{I}</math>. | ||
* Let us define the following function. | * Let us define the following function. | ||
<math>\gamma(x):= x, \text{ if } x>1/2 </math></br> | <math>\gamma(x):= \begin{cases} a\\ b \end{cases} x, \text{ if } x>1/2 </math></br> | ||
<math>\quad\quad :=g^{-1}(x), \text{ if } x\leq 1/2</math>,</br> | <math>\quad\quad :=g^{-1}(x), \text{ if } x\leq 1/2</math>,</br> | ||
where <math>g(x):= h(x)+x-1</math>, and <math>h(x):=-x\log(x)-(1-x)\log(1-x)</math>.</br> | where <math>g(x):= h(x)+x-1</math>, and <math>h(x):=-x\log(x)-(1-x)\log(1-x)</math>.</br> | ||