diff --git a/fs-succinct/succinct.tex b/fs-succinct/succinct.tex index e343276629ef3f35fd3dbf63b61a01b6e8efa7a5..b87d93fe910b32974a3f6e82cd3f75e6fcb7c09f 100644 --- a/fs-succinct/succinct.tex +++ b/fs-succinct/succinct.tex @@ -240,7 +240,8 @@ with the property that when $(m,s) = f(x,y)$, $s$ depends only on $x$. This is t that allows local decoding and modification because carry does not cascade. Internally, the a mixer is -always implemented as a composition of two mappings, $f_1$ that transforms $x \rightarrow (c,s)$ and $f2$ +always implemented as a composition of two mappings, $f_1$ that transforms $x \rightarrow +(c,s)$ and $f_2$ that transforms $(y,c) \rightarrow m$. See fig. \figref{mixer}. Both $f_1$ and $f_2$ must be injective so that the encoding is reversible. @@ -385,7 +386,7 @@ of all the mixer parameters -- i.e., a table with $\Theta(n/\log_\Sigma n)$ rows That is impractical. Note that this was not an issue for sole as there the $Y_i$'s formed an arithmetic -sequence. The weren't even the optimal $Y_i$'s that would be created by the generic +sequence. They weren't even the optimal $Y_i$'s that would be created by the generic mixer construction but a close enough approximation that still yielded good results, up to an additive constant. That was a special case -- in general, we do now know how to approximate the mixer parameters by something easier to compute locally.