Chomsky Normal Form - Converting A Grammar To Chomsky Normal Form

Converting A Grammar To Chomsky Normal Form

  1. Introduce
    Introduce a new start variable, and a new rule where is the previous start variable.
  2. Eliminate all rules
    rules are rules of the form where and where is the CFG's variable alphabet.
    Remove every rule with on its right hand side (RHS). For each rule with in its RHS, add a set of new rules consisting of the different possible combinations of replaced or not replaced with . If a rule has as a singleton on its RHS, add a new rule unless has already been removed through this process. For example, examine the following grammar :
    has one rule. When the is removed, we get the following:
    Notice that we have to account for all possibilities of and so we actually end up adding 3 rules.
  3. Eliminate all unit rules
    After all the rules have been removed, you can begin removing unit rules, or rules whose RHS contains one variable and no terminals (which is inconsistent with CNF).
    To remove
    add rule unless this is a unit rule which has already been removed.
  4. Clean up remaining rules that are not in Chomsky normal form.
    Replace with where are new variables.
    If, replace in above rules with some new variable and add rule .

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