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datovky
ds2-notes
Commits
6c223d27
Commit
6c223d27
authored
3 years ago
by
Filip Stedronsky
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Succinct: rearrange section headings
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fs-succinct/succinct.tex
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6c223d27
...
@@ -202,7 +202,7 @@ for those too.
...
@@ -202,7 +202,7 @@ for those too.
For the second pass, this is trivial, as
$
(
B
+
i
)(
B
-
i
)
=
B
^
2
-
i
^
2
\le
B
^
2
$
.
For the second pass, this is trivial, as
$
(
B
+
i
)(
B
-
i
)
=
B
^
2
-
i
^
2
\le
B
^
2
$
.
\section
{
Succinct representation of arbitrary-alphabet string
s
}
\section
{
Mixers as a building block for succinct structure
s
}
\subsection
{
A reinterpretation of the SOLE encoding
}
\subsection
{
A reinterpretation of the SOLE encoding
}
...
@@ -334,7 +334,7 @@ as promised. Note that this holds for any value of $Y$.
...
@@ -334,7 +334,7 @@ as promised. Note that this holds for any value of $Y$.
However, we cannot freely set
$
C
$
, as we have already decided that
$
C :
=
\lfloor
2
^
M
/
Y
\rfloor
$
.
However, we cannot freely set
$
C
$
, as we have already decided that
$
C :
=
\lfloor
2
^
M
/
Y
\rfloor
$
.
Instead, we need to set a value for
$
M
$
that gives us the right
$
C
$
.
Instead, we need to set a value for
$
M
$
that gives us the right
$
C
$
.
Now we are almost done.
The whole mixer parameter selection process could be as follows
The whole mixer parameter selection process could be as follows
(it may be useful to refer back to fig.
\figref
{
mixer
}
):
(it may be useful to refer back to fig.
\figref
{
mixer
}
):
\tightlist
{
n.
}
\tightlist
{
n.
}
\:
We are given
$
X
$
,
$
Y
$
as parameters.
\:
We are given
$
X
$
,
$
Y
$
as parameters.
...
@@ -346,5 +346,6 @@ All the inequalities required for mixer existence are satisfied and based on the
...
@@ -346,5 +346,6 @@ All the inequalities required for mixer existence are satisfied and based on the
above the parameters satisfy what our lemma promised.
above the parameters satisfy what our lemma promised.
\qed
\qed
\section
{
Succinct representation of arbitrary-alphabet strings
}
\endchapter
\endchapter
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