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What is the minimum number of productions present in the below given context free grammar to make it Chomsky Normal Form?
S → XYx
X → xxy
Y → Xz
S → XYx
X → xxy
Y → Xz
- a)7
- b)8
- c)9
- d)10
Correct answer is option 'B'. Can you explain this answer?
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What is the minimum number of productions present in the below given c...
Concepts:
A context-free grammar is in Chomsky Normal Form if all productions are of the form
A → BC or A → a
{A, B, C} ϵ V and a ϵ T
V is variable(non-terminal) and a is terminal
A context-free grammar is in Chomsky Normal Form if all productions are of the form
A → BC or A → a
{A, B, C} ϵ V and a ϵ T
V is variable(non-terminal) and a is terminal
Calculation:
S → XA
A → YB
B → x
X → BC
C → BD
D → y
Y → XE
E → z
S → XA
A → YB
B → x
X → BC
C → BD
D → y
Y → XE
E → z
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What is the minimum number of productions present in the below given c...
Explanation:
To convert a context-free grammar into Chomsky Normal Form, we need to ensure that all productions are in the form A -> BC or A -> a, where A, B, and C are non-terminal symbols, and a is a terminal symbol.
Minimum Number of Productions:
To convert the given context-free grammar into Chomsky Normal Form, we need to break down the productions into smaller units. Here is the breakdown of the productions:
1. S -> XY
2. X -> x
3. Y -> x
4. Y -> y
5. Y -> Z
6. Z -> a
Therefore, the minimum number of productions required to make the given context-free grammar into Chomsky Normal Form is 8.
To convert a context-free grammar into Chomsky Normal Form, we need to ensure that all productions are in the form A -> BC or A -> a, where A, B, and C are non-terminal symbols, and a is a terminal symbol.
Minimum Number of Productions:
To convert the given context-free grammar into Chomsky Normal Form, we need to break down the productions into smaller units. Here is the breakdown of the productions:
1. S -> XY
2. X -> x
3. Y -> x
4. Y -> y
5. Y -> Z
6. Z -> a
Therefore, the minimum number of productions required to make the given context-free grammar into Chomsky Normal Form is 8.
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What is the minimum number of productions present in the below given context free grammar to make it Chomsky Normal Form?S → XYxX → xxyY → Xza)7b)8c)9d)10Correct answer is option 'B'. Can you explain this answer?
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