Exercises on the Chomsky Normal Form and the CYK algorithm. Some answers
and hints. 1. Convert the following context-free grammar to Chomsky Normal ...
Exercises on the Chomsky Normal Form and the CYK algorithm Some answers and hints
1. Convert the following context-free grammar to Chomsky Normal Form: S → ab | A A → bAaA |
S0 → Xa Xb | Xb Z1 | S → Xa Xb | Xb Z1 Z1 → AZ2 | Xa A | a Z2 → Xa A | a A → Xb Z1 Xb → b Xa → a
2. Convert the following context-free grammar to Chomsky Normal Form: S → aSSa | AA A → AB | a | B → b
S0 → Xa Z1 | AA | AB | a | b | S → Xa Z1 | AA | AB | a | b A → AB | a | b Z1 → SZ2 | SXa | a Z2 → SXa | a B → b Xa → a
3. Construct CYK-tables for the strings aabb and abbb using the following grammar:
S0 → Xa Z1 | Xb S | b | S → Xa Z1 | Xb S | b Z1 → SXb | b Xb → b Xa → a
Xb , Z1 , S, S0
Xa
Xb , Z1 , S, S0
Z1 , S, S0
S, S0
Z1 , S, S0
Xa
S, S0
Xb , Z, S, S0
Xa
Xb , Z, S, S0
Z, S, S0
Xb , Z, S, S0
Z, S, S0
Z, S, S0
S, S0
Z, S, S0
Z, S, S0
4. Construct CYK-tables for the strings abbba and aaaba using the following grammar:
2
S → AY | BZ | a | b X → AY | BZ | a | b Z → XB Y
→ XA
B → b A → a
A, X, S
B, X, S
B, X, S
A, X, S
B, X, S
Z
Z
X, S
Z
Y
Y
X, S
A, X, S
A, X, S
A, X, S
A, X, S
Y
Y
X, S
3
B, X, S
Y
Z
X, S
Z
