paralell

data dependency

statement S, T,

define $S \,\delta\, T$: $T$ depends on $S$, $S$ must be executed before $T$

$S\,\delta\,T$ if and only if one of the cases are true.

$x$ is a variable

1. flow dependency: $S\,\delta^f\,T$, if $x \in OUT(S)$, and $x \in IN(T)$. and $x$ is readed in $T$

   S: x = a + b

   T: y = x

   Read after wrtie.

2. reverse dependency: $S\,\delta^a\,T$, if $x \in IN(S)$ and $x \in OUT(T)$. and $S$ read $x$ before $T$ write to $x$

   S: r = x

   T: x = a + b

   Write after read.

3. output dependency: $S\,\delta^o\,T$, if $x \in OUT(S)$ and $x \in OUT(T)$. $S$ write to $x$ before $T$ write to $x$.

   S: x = a

   T: x = b

   Write after write.