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Slides: Specialized Grammars: Linear Grammars and Normal Forms - cs wellesley

Slides: Specialized Grammars: Linear Grammars and Normal Forms - cs wellesley 2025

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The document provides an overview of specialized grammars in the context of formal languages, focusing on linear grammars, Chomsky Normal Form (CNF), and Greibach Normal Form (GNF). It explains the relationship between regular languages and context-free languages, detailing how to convert context-free grammars into CNF and GNF. The document also discusses the properties of right-linear and left-linear grammars, their equivalence to finite automata, and the process of simplifying context-free grammars by removing nullable variables and unit productions.

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What is Chomsky normal form grammar?

Converting a grammar to Chomsky normal form START: Eliminate the start symbol from right-hand sides. TERM: Eliminate rules with nonsolitary terminals. BIN: Eliminate right-hand sides with more than 2 nonterminals. DEL: Eliminate -rules. UNIT: Eliminate unit rules. Order of transformations.

How to know if a grammar is regular or not?

A grammar is regular if and only if is a single nonterminal and is a single terminal or a single terminal followed by a single nonterminal, that is a production is of the form X - a or X - aY, where X and Y are nonterminals and a is a terminal.

What is grammar and types of grammar?

Grammar is a broad term that covers all the rules of a language, including syntax, meaning, and sometimes word structure and sounds. Syntax is a part of grammar that focuses on the order and relationship of words in sentences. Syntax shows how words and phrases are arranged to form clear sentences.

What is regular grammar and its types?

Regular Grammar is the Type-3 grammar ing to Chomsky Hierarchy. They have a single non-terminal symbol on the left-hand side, a single terminal on the right-hand side, or a single terminal followed by a non-terminal. Regular Grammar accepts and generates regular languages.

Are all regular grammars linear?

All regular languages are linear; conversely, an example of a linear, non-regular language is { anbn }. as explained above.

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What is the difference between right regular grammar and extended right regular grammar?

Every strict right-regular grammar is extended right-regular, while every extended right-regular grammar can be made strict by inserting new non-terminals, such that the result generates the same language; hence, extended right-regular grammars generate the regular languages as well.

Are right linear grammars and left linear grammars equivalent?

Theorem: For every right linear grammar there is an equivalent left linear grammar (and vice versa). Proof: This will follow from other facts later. This means that the right linear languages are exactly the restricted right linear languages and are exactly the left linear languages.

Slides: Specialized Grammars: Linear Grammars and Normal Forms - cs wellesley 2025

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