Test Book Test Series

Question

Is following grammar LR(1)?

S-> asa | bS |epsilon

Comments

not lr(1)

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Bhavna.. If the grammar is LL(1)->LR(1) see the direction is one sided.. Which means if grammar is not LL(1) we cannot conclude LR(1).

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@vaibhav yes true !! It was my mistake

Answer 1

This is definitely not LL(1) because FOLLOW(S) and FIRST(S) sets are not disjoint.

It's not LR(1) also as shown in the following snapshot, there is S/R conflict in second state:

Answer 2

At initial state itself there is shift reduce conflict on lookahead symbol $. Hence not LR(1).

Comments

table will be @Ashwin Kulkarni

              a               b                  $

I0              S2                 S3                  R3

Sir, My query is how this will be Shift Reduce Conflict as there is single entry in each cell...?

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because conflict is not in state I0, it's in state I2 if you construct the table further in I2 you will get Shift-Reduce conflict

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yup Thanks i was bit confused at Intial State I0 only..

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Ashwin shift reduce conflict won't arise for $ symbol.. It will be for symbol a.. In the following state