Commit c52f9aac authored by Filip Stedronsky's avatar Filip Stedronsky
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Succinct: SOLE: fixes

parent 8bfbbb16
......@@ -172,17 +172,27 @@ increases throughout the encoding passes:
\tightlist{o}
\: If the original length was a multiple of $b$, we must add one block to complete padding.
\: We always add one block with EOF character.
\: Before the first pass, we may need to add an extra padding block to make number of blocks even.
\: Before the first pass, we may need to add an extra padding block to make number of blocks even
(not shown in fig. \figref{sole}).
\: Before the second pass, we always add an extra padding block to make number of blocks odd.
\endlist
In total, we add at most 4 blocks. Thus $r(n) \le 4b$. That is a constant
and thus we have a succinct scheme.
Also not that this representation is locally decodable and modifiable -- each input
In total, we add at most 4 blocks. Thus $r(n) \le 4b$.
For the scheme to work, we need to set $b \ge 2\log n + 2$ (so
$B \ge 4n^2$). This gives us redundancy $r(n) = \O(\log n)$. Thus
we have a succinct scheme. Also, one block fits into $\O(1)$ words
on a RAM, so we can do constant-time arithmetic on the blocks.
Note that this representation is locally decodable and modifiable -- each input
block affects at most 4 output blocks.
Now we need to check that all the alphabet translations are valid.
Now we must check that all the alphabet transformations are valid, i.e., the
output universe of each transformation is always at least as big as the input
universe.
\section{Succinct representation of arbitrary-alphabet strings}
......
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