GATE CS 2015 Set 1 — Question 28
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Compiler Design → Syntax Analysis
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Question
Which one of the following is TRUE at any valid state in shift-reduce parsing?
Correct answer
(C) The stack contains only a set of viable prefixes
Solution
Statement I: is Context-Free. All Context-Free Languages (CFLs) are recursive (decidable). The complement of a recursive language is always recursive. Thus, is recursive. Statement I is TRUE.Statement II: is Recursively Enumerable (RE) but not recursive. The complement of an RE language that is not recursive is NOT RE. Thus, is not recursive. Statement II is FALSE.Statement III: is Context-Free. The class of Context-Free Languages is not closed under complementation. Thus, is not necessarily context-free. Statement III is FALSE.Statement IV: is recursive, which implies is also RE. The complement is recursive, so is RE. is RE. The union of two RE languages is always RE. Thus, is RE. Statement IV is TRUE.Since I and IV are true, the correct option is (D).
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