GATE CS 2021 Set 2 — Question 48
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Compiler Design → Code Optimization → Liveness Analysis
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Question
For a statement in a program, in the context of liveness analysis, the following sets are defined:
: the set of variables used in
: the set of variables that are live at the entry of
: the set of variables that are live at the exit of Consider a basic block that consists of two statements, followed by . Which one of the following statements is correct?
: the set of variables used in
: the set of variables that are live at the entry of
: the set of variables that are live at the exit of Consider a basic block that consists of two statements, followed by . Which one of the following statements is correct?
Correct answer
(A) OUT(S₁) = IN(S₂)
Solution
In liveness analysis (a backward data-flow analysis), the set of variables live at the exit of a statement () is determined by the variables live at the entry of its successors. In a basic block where statements are executed sequentially, the immediate successor of statement is . The program point corresponding to the exit of is identical to the program point corresponding to the entry of . Therefore, the set of variables live at the exit of must be exactly the same as the set of variables live at the entry of . Thus, .Other options are incorrect because:
- (B) relates to of the same statement incorrectly (the standard equation is ).
- (C) and (D) introduce dependencies that do not hold for sequential execution in this manner.
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