Question:medium

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

In straight-line code (basic blocks), the OUT set of a statement equals the IN set of the next statement.
Updated On: Feb 2, 2026
  • \(OUT(S_1) = IN(S_2)\)
  • \(OUT(S_1) = IN(S_1) \cup USE(S_1)\)
  • \(OUT(S_1) = IN(S_2) \cup OUT(S_2)\)
  • \(OUT(S_1) = USE(S_1) \cup IN(S_2)\)
Show Solution

The Correct Option is A

Solution and Explanation

To determine the correct relationship between the live variable sets in the context of liveness analysis, we need to understand the relationship between the sets IN(S), OUT(S), and USE(S) for statements in basic blocks.

Liveness analysis is a data flow analysis used to determine which variables hold values that might be needed in the future. Specifically, a variable is live at a given point if its current value can be used along some path in the control flow graph.

Let's explore each of the given options:

  1. \(OUT(S_1) = IN(S_2)\): This statement is correct because directly after executing statement \(S_1\), the set of variables that are live, i.e., needed later in the program, are exactly the set of variables needed at the entry of the subsequent statement \(S_2\). Thus, \(OUT(S_1)\) must be equivalent to \(IN(S_2)\).
  2. \(OUT(S_1) = IN(S_1) \cup USE(S_1)\): This is incorrect because \(OUT(S_1)\) should not automatically include \(USE(S_1)\). \(OUT(S_1)\) is determined by what happens after \(S_1\), not merely by the union of the incoming and used variables within \(S_1\).
  3. \(OUT(S_1) = IN(S_2) \cup OUT(S_2)\): This is incorrect in this context, as there is no direct formula to compute \(OUT(S_1)\) in terms of \(IN(S_2)\) and \(OUT(S_2)\) without understanding the specifics of what happens in \(S_2\).
  4. \(OUT(S_1) = USE(S_1) \cup IN(S_2)\): This statement is incorrect because the variables that are actually live at \(OUT(S_1)\) are the ones that are determined due to being needed later in the execution, i.e., what we see as \(IN(S_2)\), rather than just the variable used in \(S_1\).

The correct answer is thus:

\(OUT(S_1) = IN(S_2)\)

This option correctly encapsulates the relationship between the liveness at the boundary of \(S_1\) and \(S_2\) within a basic block, precisely satisfying the constraints laid out by the problem.

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