Révision 193 CSL17/sequence-coding.tex
| sequence-coding.tex (revision 193) | ||
|---|---|---|
| 16 | 16 |
For an arbitrary sequence we cannot use quite the same technique since length is not determined in advance. |
| 17 | 17 |
However, by using a slightly more asymmetric encoding we can still access all required bits in quadratic modulus rather than linear, appealing to a `zig-zag' technique. |
| 18 | 18 |
|
| 19 |
\anupam{Every number is an infinite ultimately 0 sequence.}
|
|
| 19 |
\anupam{Every number is an infinite ultimately 0 sequence.}
|
|
| 20 |
|
|
| 21 |
|
|
| 22 |
\begin{definition}
|
|
| 23 |
[Sequence (de)coding] |
|
| 24 |
We define the function $\beta\bit (i,j;x,b)$, intuitively meaning ``the $j$th bit of the $i$th element of $x$ is $b$'' as $\bit \left( \frac{1}{2} (i+j)(i+j+1) +i ; x , b \right)$.
|
|
| 25 |
\end{definition}
|
|
Formats disponibles : Unified diff