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:
“Nothing is poetical if plain daylight is not poetical; and no monster should amaze us if the normal man does not amaze.”
—Gilbert Keith Chesterton (1874–1936)
“The terrorist and the policeman both come from the same basket. Revolution, legality—counter-moves in the same game; forms of idleness at bottom identical.”
—Joseph Conrad (1857–1924)