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?
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?
Show Hint
- \(OUT(S_1) = IN(S_2)\)
- \(OUT(S_1) = IN(S_1) \cup USE(S_1)\)
- \(OUT(S_1) = IN(S_2) \cup OUT(S_2)\)
- \(OUT(S_1) = USE(S_1) \cup IN(S_2)\)
The Correct Option is A
Solution and Explanation
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)
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