1 / 8

A New Normal Form for Context-Sensitive Grammars

A New Normal Form for Context-Sensitive Grammars. Presenter: Peter Varga Co-author: Benedek Nagy. Context-Free derivation trees. An upper bound can be given for the derivation tree’s depth in case of context-free grammars, if we use Chomsky normal form:.

marie
Download Presentation

A New Normal Form for Context-Sensitive Grammars

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. A New Normal Form for Context-Sensitive Grammars Presenter: Peter Varga Co-author: Benedek Nagy

  2. Context-Free derivation trees An upper bound can be given for the derivation tree’s depth in case of context-free grammars, if we use Chomsky normal form:

  3. Derivation tree for context-sensitive grammars In the case of context-sensitive grammars a derivation tree can be given as well with the use of Penttonen normal form. In this tree there will be context branches: Penttonen normal form: Aa ABC ABAC

  4. The problem is the following: A derivation of a finite word can be arbitrarily long because of those rules where the length of the left side equals with the length of the right side. Derivation tree for context-sensitive grammars

  5. In this example the depth of the tree for a finite word has to be exponentially large.

  6. Iteration-free normal form • Definition (Iteration-free normal form): A rule set called H is in iteration-free normal form, if H is in Penttonen normal form, and does not contain any context-sensitive iteration with the same context. • Theorem: Any grammar in Penttonen normal form can be derived to a grammar which is in iteration-free normal form, and the original and the derived grammar generates the same language.

  7. The derivation tree with the use of the iteration-free normal form

  8. Summary Context-free grammars Context-sensitive grammars Chomsky normal form Penttonen normal form Iteration-free normal form Finite derivation tree

More Related