Consider the control flow graph shown in the figure. Which one of the following options correctly lists the set of redundant expressions (common subexpressions) in the basic blocks B4 and B5? *Note:* All the variables are integers.

To find redundant expressions (common subexpressions) in basic blocks B4 and B5, we perform Available Expressions Analysis:

1. Basic Block B1:

   • Generates: $b + i$

   • $\text{Out}(B1) = \{ b + i \}$

2. Basic Block B2:

   • Computes: $g * k$

   • Does not kill $b + i$ (neither $b$ nor $i$ is modified).

   • $\text{Out}(B2) = \{ b + i, g * k \}$

3. Basic Block B3:

   • Computes: $g * k$

   • Computes: $c + m$, but also assigns to $b$ ($b = c + m$), which kills the expression $b + i$.

   • $\text{Out}(B3) = \{ g * k, c + m \}$

4. At the entry of Basic Block B4:

   $$\text{In}(B4) = \text{Out}(B2) \cap \text{Out}(B3) = \{ b + i, g * k \} \cap \{ g * k, c + m \} = \{ g * k \}$$

   • Inside B4:

     • The expression $g * k$ in $x = g * k$ is already available from all incoming paths ($\{ g * k \} \in \text{In}(B4)$), so **$g * k$ is a redundant common subexpression**.

     • The expression $b + i$ in $y = b + i$ is NOT available because it was killed along the path through B3.

   • Redundant expressions in **B4 = $\{ g * k \}$**.

5. At the entry of Basic Block B5:

   • B4 generates $b + i$, so $\text{Out}(B4) = \{ g * k, b + i \}$.

   • $\text{In}(B5) = \text{Out}(B4) = \{ g * k, b + i \}$.

   • Inside B5, the expression evaluated is $c + m$. Since $c + m \notin \text{In}(B5)$, it is not redundant.

   • Redundant expressions in B5 = $\{ \}$.

Thus, the correct option is (D).