Chomsky Normal Form

Named after Noam Chomsky (b. 1928), American linguist and philosopher, who first described it.

Chomsky Normal Form (uncountable)

1. (computing theory) A context-free grammar in which the right hand side of any production rule consists of either one terminal symbol or two non-terminal symbols.

   Any ε-free Context Free Grammar can be converted (through an algorithm) into one in Chomsky Normal Form, and there is an algorithm that can parse formulas in the language of such a grammar in polynomial time; it is called the CYK algorithm.

2. (computing theory) A context-free grammar in which the right hand side of any production rule consists of either one terminal symbol or two non-terminal symbols (neither of which is the start symbol) or the epsilon (i.e. null string) symbol, but only if the left hand side is the start symbol. (Note: this is the full-fledged version, whereas the previous definition may be said to be defining Chomsky reduced form.)