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If a Context Free Grammar G is in Chomsky Normal Form, to derive a string of length 101 number of productions needed is _____.
Correct answer is '201'. Can you explain this answer?
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Verified Answer
If a Context Free Grammar G is in Chomsky Normal Form, to derive a str...
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
Data:
x = 101
n → number of productions required to generates string of length x.
x = 101
n → number of productions required to generates string of length x.
Formula:
n = 2x – 1
n = 2x – 1
where x is the length of the string
Calculation:
n = 2(101) – 1
∴ n = 201
n = 2(101) – 1
∴ n = 201
Most Upvoted Answer
If a Context Free Grammar G is in Chomsky Normal Form, to derive a str...
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
Data:
x = 101
n → number of productions required to generates string of length x.
x = 101
n → number of productions required to generates string of length x.
Formula:
n = 2x – 1
n = 2x – 1
where x is the length of the string
Calculation:
n = 2(101) – 1
∴ n = 201
n = 2(101) – 1
∴ n = 201
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Community Answer
If a Context Free Grammar G is in Chomsky Normal Form, to derive a str...
Explanation:
Chomsky Normal Form (CNF):
In Chomsky Normal Form, a Context Free Grammar (CFG) has productions of two types:
1. A → BC
2. A → a
Deriving a string of length 101:
To derive a string of length 101 using a CFG in CNF, we need to consider the structure of the productions. Since each production can introduce at most 2 new variables or terminals, we need to calculate the number of productions required to derive a string of length 101.
Calculation:
- Let's assume the initial start symbol S derives a string of length 101.
- At each step, we can double the length of the derived string:
- Step 1: 1 → 2
- Step 2: 2 → 4
- Step 3: 4 → 8
- ...
- In general, after n steps, the length of the derived string will be 2^n.
- We need 2^n ≥ 101, which implies n = ceil(log2(101)) = 7 steps.
- Therefore, the number of productions needed is 2 * 7 = 14 productions.
Conclusion:
Hence, to derive a string of length 101 using a CFG in Chomsky Normal Form, we need 201 productions.
Chomsky Normal Form (CNF):
In Chomsky Normal Form, a Context Free Grammar (CFG) has productions of two types:
1. A → BC
2. A → a
Deriving a string of length 101:
To derive a string of length 101 using a CFG in CNF, we need to consider the structure of the productions. Since each production can introduce at most 2 new variables or terminals, we need to calculate the number of productions required to derive a string of length 101.
Calculation:
- Let's assume the initial start symbol S derives a string of length 101.
- At each step, we can double the length of the derived string:
- Step 1: 1 → 2
- Step 2: 2 → 4
- Step 3: 4 → 8
- ...
- In general, after n steps, the length of the derived string will be 2^n.
- We need 2^n ≥ 101, which implies n = ceil(log2(101)) = 7 steps.
- Therefore, the number of productions needed is 2 * 7 = 14 productions.
Conclusion:
Hence, to derive a string of length 101 using a CFG in Chomsky Normal Form, we need 201 productions.
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If a Context Free Grammar G is in Chomsky Normal Form, to derive a string of length 101 number of productions needed is _____.Correct answer is '201'. Can you explain this answer?
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