CFG to CNF

CFG to CNF

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  GROUP MEMBERS ▪ ZainUL Abideen (BSSE-FA17-048)
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  Theory Of Automata ■ Presentation
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  CFGTO CNF
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  CFG CFG stands forcontext-free grammar. It is a formal grammar which is used to generate all possible patterns of strings in a given formal language.
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  CFG Context-free grammar Gcan be defined by four tuples as G = (V, T, P, S)
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  CFG G is thegrammar, which consists of a set of the production rule. It is used to generate the string of a language. T is the final set of a terminal symbol. It is denoted by lower case letters. V is the final set of a non-terminal symbol. It is denoted by capital letters. P is a set of production rules, which is used for replacing non-terminals symbols(on the left side of the production) in a string with other terminal or non-terminal symbols(on the right side of the production). S is the start symbol which is used to derive the string. We can derive the string by repeatedly replacing a non- terminal by the right-hand side of the production until all non-terminal have been replaced by terminal symbols.
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  CNF CNF stands forChomsky normal form. A CFG(context free grammar) is in CNF(Chomsky normal form) if all production rules satisfy one of the following conditions: • Start symbol generating ε. For example, A → ε. • A non-terminal generating two non-terminals. For example, S → AB. • A non-terminal generating a terminal. For example, S → a.
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  CONVERTTING CFGTO CNF
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  Steps for convertingCFG into CNF ■ Step 1: Eliminate start symbol from the RHS. If the start symbolT is at the right-hand side of any production, create a new production as: S1 → S ■ Where S1 is the new start symbol. ■ Step 2: In the grammar, remove the null, unit and useless productions.You can refer to the Simplification of CFG. ■ Step 3: Eliminate terminals from the RHS of the production if they exist with other non- terminals or terminals. For example, production S → aA can be decomposed as: ■ S → RA ■ R → a ■ Step 4: Eliminate RHS with more than two non-terminals. For example, S → ASB can be decomposed as: ■ S → RS ■ R → AS
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  EXAMPLE Convert the givenCFG to CNF. Consider the given grammar G1: S → a | aA | B A → aBB | ε B → Aa | b
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  SOLUTION: Step 1: Wewill create a new production S1 → S, as the start symbol S appears on the RHS. The grammar will be: S1 → S S → a | aA | B A → aBB | ε B → Aa | b
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  Step 2: Asgrammar G1 contains A → ε null production, its removal from the grammar yields: S1 → S S → a | aA | B A → aBB B → Aa | b | a Now, as grammar G1 contains Unit production S → B, its removal yield: S1 → S S → a | aA | Aa | b A → aBB B → Aa | b | a Also remove the unit production S1 → S, its removal from the grammar yields: S0 → a | aA | Aa | b S → a | aA | Aa | b A → aBB B → Aa | b | a
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  Step 3: Inthe production rule S0 → aA | Aa, S → aA | Aa, A → aBB and B → Aa, terminal a exists on RHS with non-terminals. So we will replace terminal a with X: S0 → a | XA | AX | b S → a | XA | AX | b A → XBB B → AX | b | a X → a Step 4: In the production rule A → XBB, RHS has more than two symbols, removing it from grammar yield: S0 → a | XA | AX | b S → a | XA | AX | b A → RB B → AX | b | a X → a R → XB Hence, for the given grammar, this is the required CNF.
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  END OF Presentation THANK YOU