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A CFG (Context Free Grammar) is said to be in Chomsky Normal Form (CNF), if all the productions are of the form A → BC or A → a. Let G be a CFG in CNF. To derive a string of terminals of length x, the number of products to be used is
- a)2x - 1
- b)2x
- c)2x + 1
- d)2
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A CFG (Context Free Grammar) is said to be in Chomsky Normal Form (CNF...
Concept:
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
Formula:
n = 2x - 1
number of productions required to generates string of length x.
where x is the length of the string
n = 2x - 1
number of productions required to generates string of length x.
where x is the length of the string
Example:
Production:
S → XY
X → a
Y → b
Derive the string ab
S → XY
S → aY
S → ab
Number of productions needed = 3
Verification
2x - 1 = 2(2) - 1 = 3
Production:
S → XY
X → a
Y → b
Derive the string ab
S → XY
S → aY
S → ab
Number of productions needed = 3
Verification
2x - 1 = 2(2) - 1 = 3
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Community Answer
A CFG (Context Free Grammar) is said to be in Chomsky Normal Form (CNF...
→ BC or A → a, where A, B, and C are non-terminals, and a is a terminal symbol. Additionally, the start symbol S is allowed to appear on the right-hand side of productions.
CNF is a restricted form of CFG that simplifies the parsing process for certain algorithms. It has some advantages, such as being able to parse in O(n^3) time complexity. However, not all CFGs can be converted to CNF without changing the language generated by the grammar.
To convert a CFG to CNF, the following steps are typically followed:
1. Eliminate ε-productions: Remove any production of the form A → ε, where ε represents the empty string. This is done by adding new productions to account for the empty string.
2. Eliminate unit productions: Remove any production of the form A → B, where A and B are non-terminals. This is done by replacing each unit production with the productions of the non-terminal it generates.
3. Introduce new non-terminals: If a production has more than two non-terminals on the right-hand side, introduce new non-terminals to reduce it to two non-terminals. For example, if a production is of the form A → BCDE, introduce a new non-terminal X and replace it with A → BX and X → CDE. Repeat this step until all productions have at most two non-terminals on the right-hand side.
4. Convert terminals: If a production has a terminal symbol on the right-hand side, replace it with a new non-terminal and a production that generates that terminal. For example, if a production is of the form A → a, introduce a new non-terminal X and replace it with A → X and X → a.
After following these steps, the CFG will be in CNF. It is important to note that the resulting CNF may generate the same language as the original CFG, but the parse trees may differ due to the introduced non-terminals.
CNF is a restricted form of CFG that simplifies the parsing process for certain algorithms. It has some advantages, such as being able to parse in O(n^3) time complexity. However, not all CFGs can be converted to CNF without changing the language generated by the grammar.
To convert a CFG to CNF, the following steps are typically followed:
1. Eliminate ε-productions: Remove any production of the form A → ε, where ε represents the empty string. This is done by adding new productions to account for the empty string.
2. Eliminate unit productions: Remove any production of the form A → B, where A and B are non-terminals. This is done by replacing each unit production with the productions of the non-terminal it generates.
3. Introduce new non-terminals: If a production has more than two non-terminals on the right-hand side, introduce new non-terminals to reduce it to two non-terminals. For example, if a production is of the form A → BCDE, introduce a new non-terminal X and replace it with A → BX and X → CDE. Repeat this step until all productions have at most two non-terminals on the right-hand side.
4. Convert terminals: If a production has a terminal symbol on the right-hand side, replace it with a new non-terminal and a production that generates that terminal. For example, if a production is of the form A → a, introduce a new non-terminal X and replace it with A → X and X → a.
After following these steps, the CFG will be in CNF. It is important to note that the resulting CNF may generate the same language as the original CFG, but the parse trees may differ due to the introduced non-terminals.
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A CFG (Context Free Grammar) is said to be in Chomsky Normal Form (CNF), if all the productions are of the form A → BC or A → a. Let G be a CFG in CNF. To derive a string of terminals of length x, the number of products to be used isa)2x - 1b)2xc)2x + 1d)2Correct answer is option 'A'. Can you explain this answer?
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A CFG (Context Free Grammar) is said to be in Chomsky Normal Form (CNF), if all the productions are of the form A → BC or A → a. Let G be a CFG in CNF. To derive a string of terminals of length x, the number of products to be used isa)2x - 1b)2xc)2x + 1d)2Correct answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about A CFG (Context Free Grammar) is said to be in Chomsky Normal Form (CNF), if all the productions are of the form A → BC or A → a. Let G be a CFG in CNF. To derive a string of terminals of length x, the number of products to be used isa)2x - 1b)2xc)2x + 1d)2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A CFG (Context Free Grammar) is said to be in Chomsky Normal Form (CNF), if all the productions are of the form A → BC or A → a. Let G be a CFG in CNF. To derive a string of terminals of length x, the number of products to be used isa)2x - 1b)2xc)2x + 1d)2Correct answer is option 'A'. Can you explain this answer?.
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