Kuroda normal form

1

In formal language theory, a noncontracting grammar is in Kuroda normal form if all production rules are of the form: where A, B, C and D are nonterminal symbols and a is a terminal symbol. Some sources omit the A → B pattern. It is named after Sige-Yuki Kuroda, who originally called it a linear bounded grammar, a terminology that was also used by a few other authors thereafter. Every grammar in Kuroda normal form is noncontracting, and therefore, generates a context-sensitive language. Conversely, every noncontracting grammar that does not generate the empty string can be converted to Kuroda normal form. A straightforward technique attributed to György Révész transforms a grammar in Kuroda normal form to a context-sensitive grammar: AB → CD is replaced by four context-sensitive rules AB → AZ, AZ → WZ, WZ → WD and WD → CD. This proves that every noncontracting grammar generates a context-sensitive language. There is a similar normal form for unrestricted grammars as well, which at least some authors call "Kuroda normal form" too: where ε is the empty string. Every unrestricted grammar is weakly equivalent to one using only productions of this form. If the rule AB → CD is eliminated from the above, one obtains context-free grammars in Chomsky Normal Form. The Penttonen normal form (for unrestricted grammars) is a special case where first rule above is AB → AD. Similarly, for context-sensitive grammars, the Penttonen normal form, also called the one-sided normal form (following Penttonen's own terminology) is: For every context-sensitive grammar, there exists a weakly equivalent one-sided normal form.

This article is derived from Wikipedia and licensed under CC BY-SA 4.0. View the original article.

Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc.
Bliptext is not affiliated with or endorsed by Wikipedia or the Wikimedia Foundation.

View original