In formal language theory, a context-free grammar is said to be in Chomsky normal form if all of its production rules are of the form:
- or
- or
where, and are nonterminal symbols, α is a terminal symbol (a symbol that represents a constant value), is the start symbol, and ε is the empty string. Also, neither nor may be the start symbol, and the third production rule can only appear if ε is in L(G), namely, the language produced by the Context-Free Grammar G.
Every grammar in Chomsky normal form is context-free, and conversely, every context-free grammar can be transformed into an equivalent one which is in Chomsky normal form. Several algorithms for performing such a transformation are known. Transformations are described in most textbooks on automata theory, such as Hopcroft and Ullman, 1979. As pointed out by Lange and Leiß, the drawback of these transformations is that they can lead to an undesirable bloat in grammar size. The size of a grammar is the sum of the sizes of its production rules, where the size of a rule is one plus the length of its right-hand side. Using to denote the size of the original grammar, the size blow-up in the worst case may range from to, depending on the transformation algorithm used.
Read more about Chomsky Normal Form: Alternative Definition, Converting A Grammar To Chomsky Normal Form
Famous quotes containing the words chomsky, normal and/or form:
“Hence, a generative grammar must be a system of rules that can iterate to generate an indefinitely large number of structures. This system of rules can be analyzed into the three major components of a generative grammar: the syntactic, phonological, and semantic components.”
—Noam Chomsky (b. 1928)
“As blacks, we need not be afraid that encouraging moral development, a conscience and guilt will prevent social action. Black children without the ability to feel a normal amount of guilt will victimize their parents, relatives and community first. They are unlikely to be involved in social action to improve the black community. Their self-centered personalities will cause them to look out for themselves without concern for others, black or white.”
—James P. Comer (20th century)
“The novel is the highest form of human expression so far attained. Why? Because it is so incapable of the absolute.”
—D.H. (David Herbert)