Consider the following intermediate program in three address code $p = a - b$ $q = p * c$ $p = u * v$ $q = p + q$ Which one of the following corresponds to a static single assignment form of the above code?

In Static Single Assignment (SSA) form, each variable is defined (assigned) exactly once, and every use of a variable refers to a unique reaching definition [INDEX_0]. Subscripts are typically introduced to distinguish different definitions of the same original variable [INDEX_0].

Let us trace the original program step-by-step:

1. $p = a - b$: A new definition for $p$. Introduce a unique variable name, say $p_3$.

   $$\implies p_3 = a - b$$

2. $q = p * c$: A new definition for $q$, and it uses the value of $p$ defined in step 1 ($p_3$). Introduce a unique name for $q$, say $q_4$.

   $$\implies q_4 = p_3 * c$$

3. $p = u * v$: A new definition for $p$. It must receive a fresh subscript distinct from previous definitions, say $p_4$.

   $$\implies p_4 = u * v$$

4. $q = p + q$: A new definition for $q$. It must receive a fresh subscript, say $q_5$. It uses the most recent definition of $p$ (from step 3, $p_4$) and the most recent definition of $q$ (from step 2, $q_4$).

   $$\implies q_5 = p_4 + q_4$$

Combining these gives the SSA form:

This matches option (B).

### Why other options are incorrect:

• (A) violates the single assignment rule because $p_1$ and $q_1$ are assigned multiple times.

• (C) uses undefined variable versions ($p_2$ in line 2, and $p_4, q_3$ in line 4).

• (D) fails to rename variables at their uses in lines 2 and 4.