Parsing Table - Automata and Complexity Theory - Lecture Slides, Slides of Theory of Automata

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LR(0) Parsing Table

Department of Computer Science & Engineering

LR(0) Example

• Given grammar G:

• S →a A c B e
• A →b
• A →A b
• B →d

• Construct the deterministic PDA that parse.

• Show the parsing process for string abbcde

and abbce

Parsing Table

ACTION GOTO a c e b d # S A B 0 S 2 1 1 acc 2 S 4 3 3 S 5 S 6 4 r 2 r 2 r 2 r 2 r 2 r 2 5 S 8 7 6 r 3 r 3 r 3 r 3 r 3 r 3 7 S 9 8 r 4 r 4 r 4 r 4 r 4 r 4 9 r 1 r 1 r 1 r 1 r 1 r 1

Parsing abbcde

• 1 0 # abbcde# s Step states. Syms. The rest of input action goto
• 2 02 #a bbcde# s
• 3 024 #ab bcde# r2
• 4 023 #aA bcde# s
• 5 0236 #aAb cde# r3
• 6 023 #aA cde# s
• 7 0235 #aAc de# s
• 8 02358 #aAcd e# r4
• 9 02357 #aAcB e# s
• 10 023579 #aAcBe # r1

Practice

• Grammar G:

• (0) S`→E (1) E→aA (2) E→bB
• (3) A→cA (4) A→d (5) B→cB
• (7) B→d

• PDA states for LR(0):

• I 0 : S→** ．E I 1 **: S→E ． I 2 : E→a ．A
• E→ ． aA A→.cA
• E→ ． bB A→ ．d

PDA states cont.

I 3 : E→b ．B I4 : A→c .A I 5 : B→c ．B

B→ ．cB A→ ．cA B→ ．cB

B→ ．d A → .d B→ ．d

I 6 : E →aA ． I 7 : E →bB ． I 8 : A →cA ．

I 9 : B →cB ． I10 : A→d ． I 11 : B→d ．