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Let G be a Context Free Grammar in Chomsky Normal Form. To derive a string (aaaaaa)n where a is terminal variable and n is 5, the number of products to be used is _____.
Correct answer is '59'. Can you explain this answer?
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Let G be a Context Free Grammar in Chomsky Normal Form. To derive a st...
Solution:
Chomsky Normal Form of a Context Free Grammar allows only two types of productions:
1. A → BC
2. A → a
where A, B, and C are non-terminal variables and a is a terminal variable.
To derive a string (aaaaaa)n where a is terminal variable and n is 5, we can follow the following steps:
Step 1: Start with the start variable S and apply the production S → AB where A and B are two new variables.
Step 2: Apply the production A → a and B → CD where C and D are two new variables.
Step 3: Apply the production C → a and D → EF where E and F are two new variables.
Step 4: Apply the production E → a and F → GH where G and H are two new variables.
Step 5: Apply the production G → a and H → IJ where I and J are two new variables.
Step 6: Apply the production I → a and J → a.
Step 7: Repeat steps 5 and 6 n-1 times to get the string (aaaaaa)n.
So, to derive the string (aaaaaa)5, we need to use a total of 59 productions.
Therefore, the correct answer is '59'.
Chomsky Normal Form of a Context Free Grammar allows only two types of productions:
1. A → BC
2. A → a
where A, B, and C are non-terminal variables and a is a terminal variable.
To derive a string (aaaaaa)n where a is terminal variable and n is 5, we can follow the following steps:
Step 1: Start with the start variable S and apply the production S → AB where A and B are two new variables.
Step 2: Apply the production A → a and B → CD where C and D are two new variables.
Step 3: Apply the production C → a and D → EF where E and F are two new variables.
Step 4: Apply the production E → a and F → GH where G and H are two new variables.
Step 5: Apply the production G → a and H → IJ where I and J are two new variables.
Step 6: Apply the production I → a and J → a.
Step 7: Repeat steps 5 and 6 n-1 times to get the string (aaaaaa)n.
So, to derive the string (aaaaaa)5, we need to use a total of 59 productions.
Therefore, the correct answer is '59'.
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Community Answer
Let G be a Context Free Grammar in Chomsky Normal Form. To derive a st...
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:
Since n = 5
(aaaaaa)5
Length of string = x = 30
Since n = 5
(aaaaaa)5
Length of string = x = 30
Formula:
The number of products used = 2x – 1
where x is the length of the string
The number of products used = 2x – 1
where x is the length of the string
Calculation:
number of products = 2x – 1 = 2 × 30 – 1 = 59
number of products = 2x – 1 = 2 × 30 – 1 = 59
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Let G be a Context Free Grammar in Chomsky Normal Form. To derive a string (aaaaaa)n where a is terminal variable and n is 5, the number of products to be used is _____.Correct answer is '59'. Can you explain this answer?
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