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Consider the CFG with {S,A,B) as the non-terminal alphabet, {a,b, ε) as the terminal alphabet, S as the start symbol and the following set of production rules S → ASA | aB | b A → B B → b | ∈ Convert the given grammar into CNF?
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Consider the CFG with {S,A,B) as the non-terminal alphabet, {a,b, ε) a...
Conversion of CFG to CNF
Step 1: Elimination of ε productions
- The given grammar has ε production in the production rules of B. We need to eliminate it.
- We can replace B → ε with two productions B → b and B → BB.
- After this step, the production rules become:
- S → ASA | aB | b
- A → B
- B → b | B B
Step 2: Elimination of unit productions
- There are no unit productions in the given grammar.
Step 3: Elimination of non-terminal symbols with more than 2 terminals
- There are no production rules with more than 2 non-terminals in the given grammar.
Step 4: Conversion of remaining productions to CNF
- We need to convert the remaining production rules to CNF.
- The production S → ASA has 3 non-terminals. We can introduce a new non-terminal symbol C and replace S → ASA with S → AC and C → SA.
- After this step, the production rules become:
- S → AC | aB | b
- A → B
- B → b | BB
- C → SA
Final CNF form of the given grammar
- The final form of the given grammar in CNF is:
- S → AC | aB | b
- A → B
- B → b | BB
- C → SA
- A → C
- S → A
- S → B
- C → B
Step 1: Elimination of ε productions
- The given grammar has ε production in the production rules of B. We need to eliminate it.
- We can replace B → ε with two productions B → b and B → BB.
- After this step, the production rules become:
- S → ASA | aB | b
- A → B
- B → b | B B
Step 2: Elimination of unit productions
- There are no unit productions in the given grammar.
Step 3: Elimination of non-terminal symbols with more than 2 terminals
- There are no production rules with more than 2 non-terminals in the given grammar.
Step 4: Conversion of remaining productions to CNF
- We need to convert the remaining production rules to CNF.
- The production S → ASA has 3 non-terminals. We can introduce a new non-terminal symbol C and replace S → ASA with S → AC and C → SA.
- After this step, the production rules become:
- S → AC | aB | b
- A → B
- B → b | BB
- C → SA
Final CNF form of the given grammar
- The final form of the given grammar in CNF is:
- S → AC | aB | b
- A → B
- B → b | BB
- C → SA
- A → C
- S → A
- S → B
- C → B
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Consider the CFG with {S,A,B) as the non-terminal alphabet, {a,b, ε) as the terminal alphabet, S as the start symbol and the following set of production rules S → ASA | aB | b A → B B → b | ∈ Convert the given grammar into CNF?
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Consider the CFG with {S,A,B) as the non-terminal alphabet, {a,b, ε) as the terminal alphabet, S as the start symbol and the following set of production rules S → ASA | aB | b A → B B → b | ∈ Convert the given grammar into CNF? 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 Consider the CFG with {S,A,B) as the non-terminal alphabet, {a,b, ε) as the terminal alphabet, S as the start symbol and the following set of production rules S → ASA | aB | b A → B B → b | ∈ Convert the given grammar into CNF? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the CFG with {S,A,B) as the non-terminal alphabet, {a,b, ε) as the terminal alphabet, S as the start symbol and the following set of production rules S → ASA | aB | b A → B B → b | ∈ Convert the given grammar into CNF?.
Consider the CFG with {S,A,B) as the non-terminal alphabet, {a,b, ε) as the terminal alphabet, S as the start symbol and the following set of production rules S → ASA | aB | b A → B B → b | ∈ Convert the given grammar into CNF? 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 Consider the CFG with {S,A,B) as the non-terminal alphabet, {a,b, ε) as the terminal alphabet, S as the start symbol and the following set of production rules S → ASA | aB | b A → B B → b | ∈ Convert the given grammar into CNF? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the CFG with {S,A,B) as the non-terminal alphabet, {a,b, ε) as the terminal alphabet, S as the start symbol and the following set of production rules S → ASA | aB | b A → B B → b | ∈ Convert the given grammar into CNF?.
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