Question

For a statement \(S\) in a program, in the context of liveness analysis, the following sets are defined: 
\(USE(S)\) :  the set of variables used in \(S\) 
\(IN(S)\) :  the set of variables that are live at the entry of \(S\) 
\(OUT(S)\) :  the set of variables that are live at the exit of \(S\) 

Consider a basic block that consists of two statements, \(S_1\) followed by \(S_2\). Which one of the following statements is correct?

• A. \(OUT(S_1) = IN(S_2)\)
• B. \(OUT(S_1) = IN(S_1) \cup USE(S_1)\)
• C. \(OUT(S_1) = IN(S_2) \cup OUT(S_2)\)
• D. \(OUT(S_1) = USE(S_1) \cup IN(S_2)\)

Hint:

In straight-line code (basic blocks), the OUT set of a statement equals the IN set of the next statement.

Answer 1

The Correct Option is A

Step 1: Property of a basic block.
In a basic block, control flows sequentially from one statement to the next without any branching. Hence, the exit of \(S_1\) directly connects to the entry of \(S_2\).

Step 2: Liveness flow equation.
By definition of liveness analysis, the variables live at the exit of \(S_1\) are exactly the variables live at the entry of the immediately following statement \(S_2\).

Step 3: Elimination of other options.
Options (B), (C), and (D) do not correspond to standard liveness flow equations used in data-flow analysis.

Step 4: Conclusion.
Therefore, the correct relation is \(OUT(S_1) = IN(S_2)\).

Final Answer: (A)