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Let G be the following grammar: 1. S T 2. T O 3. T T 4. O V = E i [ E ] 5. V i 6. V i 7. E ( E) 8. E Construct the LR(0) DFA

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Answer #1

a)

b)

LR(0) parsing table:

( ) ; = [ ] i $ E O S T V
0 s5 1 2 3 4
1 r2 r2 r2 r2 r2 r2 r2 r2
2 acc
3 r1 r1 s6/r1 r1 r1 r1 r1 r1
4 s7
5 r6 r6 r6 r6 s8/r6 r6 r6 r6
6 s5 9 4
7 s10 s12 11
8 s10 s12 13
9 r3 r3 r3 r3 r3 r3 r3 r3
10 s10 s12 14
11 r4 r4 r4 r4 r4 r4 r4 r4
12 r7 r7 r7 r7 r7 r7 r7 r7
13 s15
14 s16
15 r5 r5 r5 r5 r5 r5 r5 r5
16 r8 r8 r8 r8 r8 r8 r8 r8

Row(5,[) - has shift reduce conflict

Row(3,;) - has shift reduce conflict

LR(0) parsing table has shift reduce conflicts, so we need to make SLR(1) parsing table.

Computing FIRST and FOLLOW

FOLLOW FIRST { $. ), i. ]} S.:) =

SLR(1) parsing table is as follows:

$ i E S T s5 r2 r2 s7 s8 s5 s10 s12 1 s10 $12 13 r3 r3 14 10 s10 $12 11 r4 r4 12 r7 r7 13 s15 s16 14 r5 16 r8 rf r8

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