Context-free Grammar - Normal Forms

Normal Forms

Every context-free grammar that does not generate the empty string can be transformed into one in which no rule has the empty string as a product . If it does generate the empty string, it will be necessary to include the rule, but there need be no other ε-rule. Every context-free grammar with no ε-production has an equivalent grammar in Chomsky normal form or Greibach normal form. "Equivalent" here means that the two grammars generate the same language.

Because of the especially simple form of production rules in Chomsky Normal Form grammars, this normal form has both theoretical and practical implications. For instance, given a context-free grammar, one can use the Chomsky Normal Form to construct a polynomial-time algorithm that decides whether a given string is in the language represented by that grammar or not (the CYK algorithm).

Read more about this topic:  Context-free Grammar

Famous quotes containing the words normal and/or forms:

    In order to move others deeply we must deliberately allow ourselves to be carried away beyond the bounds of our normal sensibility.
    Joseph Conrad (1857–1924)

    Our normal waking consciousness, rational consciousness as we call it, is but one special type of consciousness, whilst all about it, parted from it by the filmiest of screens, there lie potential forms of consciousness entirely different.
    William James (1842–1910)