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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
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
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-terminal symbols and a is a terminal symbol.
In CNF, each production rule has two non-terminal symbols on the right-hand side or one terminal symbol. This form allows for easier parsing and analysis of the grammar.
To convert a CFG into CNF, the following steps can be followed:
1. Eliminate ε-productions: Remove any productions of the form A -> ε, where ε represents the empty string. If a non-terminal symbol A can derive ε, then for every production rule B -> αAβ, add a new production rule B -> αβ.
2. Eliminate unit productions: Remove any unit productions of the form A -> B, where A and B are non-terminal symbols. For every unit production rule A -> B, add all the productions of B to A.
3. Eliminate terminals in right-hand side: Replace any production rule A -> a, where a is a terminal symbol, with a new non-terminal symbol X and a production rule X -> a.
4. Convert long productions: For any production rule A -> B1B2...Bn, where n > 2, introduce new non-terminal symbols Xi for each Bi except for the last one. Replace the original production rule with A -> B1X1, X1 -> B2X2, X2 -> B3X3, and so on until the last one, Xn-2 -> Bn-1Bn.
5. The CFG is now in CNF.
This process guarantees that all productions are either of the form A -> BC or A -> a, where A, B, and C are non-terminal symbols and a is a terminal symbol.
In CNF, each production rule has two non-terminal symbols on the right-hand side or one terminal symbol. This form allows for easier parsing and analysis of the grammar.
To convert a CFG into CNF, the following steps can be followed:
1. Eliminate ε-productions: Remove any productions of the form A -> ε, where ε represents the empty string. If a non-terminal symbol A can derive ε, then for every production rule B -> αAβ, add a new production rule B -> αβ.
2. Eliminate unit productions: Remove any unit productions of the form A -> B, where A and B are non-terminal symbols. For every unit production rule A -> B, add all the productions of B to A.
3. Eliminate terminals in right-hand side: Replace any production rule A -> a, where a is a terminal symbol, with a new non-terminal symbol X and a production rule X -> a.
4. Convert long productions: For any production rule A -> B1B2...Bn, where n > 2, introduce new non-terminal symbols Xi for each Bi except for the last one. Replace the original production rule with A -> B1X1, X1 -> B2X2, X2 -> B3X3, and so on until the last one, Xn-2 -> Bn-1Bn.
5. The CFG is now in CNF.
This process guarantees that all productions are either of the form A -> BC or A -> a, where A, B, and C are non-terminal symbols and a is a terminal symbol.
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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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