GATE1988-10ia

Question

Consider the following grammar:

• $S \rightarrow S$
• $S \rightarrow SS \mid a \mid \epsilon$

Construct the collection of sets of LR (0) items for this grammar and draw its goto graph.

Comments

i think this is ambigous grammer try to gererate string "a" you will gate 2 LMD

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It is ambiguous grammar and we can't parse it by LR(0) parser. right na?

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Here  S→  ϵ will take as reduce/ shift action or not effect on LR(0) DFA??

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So we cannot write LR(0) items if grammar is ambiguous?

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afaik, LR(0) items can be constructed if the grammar is ambiguous.

Answer 1

The augmented production is $S^{'} \rightarrow S$.

$\textbf{GOTO Graph:}$

Here, each of $I_0$, $I_1$, $I_2$, $I_3$ is a set of $LR(0)$ items. And hence $I_0$, $I_1$, $I_2$, $I_3$ are the collection of sets of $LR(0)$ items.

Comments

The grammar is not LR(0) right?

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No, it's not. I0, I1, and I3 have shift-reduce conflicts.

Answer 2

Augmented production S'-->S

 

Comments

Sir we can write LR(0) items..

But there will be conflicts in dfa (of canonical collection of LR(0) items).. so the grammar will not be LR(0)

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Thats all is asked in the question rt?

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Yes..

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Yes this grammar is not LR(0)

And the question only asked to draw the DFA