Let's break down the problem step by step. ### **Given Definitions** - **USE(S):** Variables used in statement S. - **IN(S):** Variables that are live at the entry of S. - **OUT(S):** Variables that are live at the exit of S. ### **Liveness Analysis Equations** For a statement S: - \(\text{IN}(S) = \text{USE}(S) \cup (\text{OUT}(S) - \text{DEF}(S))\) - \(\text{OUT}(S)\) for a statement is the set of variables live at entry of its successor. ### **For Two Statements: S1 followed by S2** - S1 is followed by S2, so the successor of S1 is S2. - Thus, **OUT(S1) = IN(S2)** ### **Matching with Options** Let's check each option: - **A: OUT(S1) = IN(S2)** This matches our conclusion above. - **B: OUT(S1) = IN(S1) ∪ USE(S1)** This is not a standard liveness equation. - **C: OUT(S1) = IN(S2) ∪ OUT(S2)** This is not correct. - **D: OUT(S1) = USE(S1) ∪ IN(S2)** This is not correct. --- ## **Final Answer** ### **The correct answer is:** > **A. OUT(S1) = IN(S2)** --- #### **Reasoning** In a basic block, the OUT set of a statement is the IN set of its immediate successor. So for S1 followed by S2: **OUT(S1) = IN(S2)** --- **Reference: Compiler Design, Liveness Analysis (Data Flow Analysis)**