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Give the properties of Type 1 and Type 2 grammars from the Chomsky Hierarchy of grammars.

According to Chomsky hierarchy, grammar is divided into 4 types as follows: 

  1. Type 0 is known as unrestricted grammar.

  2. Type 1 is known as context-sensitive grammar.

  3. Type 2 is known as a context-free grammar.

  4. Type 3 Regular Grammar.

Here are the properties of Type 1 and Type 2 grammars:

Type 1 (Context-Sensitive Grammar):

  1. Generative Power: Type 1 grammars can generate context-sensitive languages.

  2. Rules: Production rules in Type 1 grammars are of the form α → β, where α is a non-empty string of symbols, and β is another non-empty string of symbols. However, the length of α must be less than or equal to that of β.

  3. Context Sensitivity: The rules in Type 1 grammar allow for contextual constraints, where the rewriting of symbols depends on the surrounding context.

  4. Languages: Type 1 grammars can generate more complex languages than Type 2 (context-free) grammars, including natural languages and some programming languages.

Type 2 (Context-Free Grammar):

  1. Generative Power: Type 2 grammars can generate context-free languages.

  2. Rules: Production rules in Type 2 grammars are of the form A → γ, where A is a single non-terminal symbol, and γ is a string of terminals and/or non-terminals. In other words, the rewriting of symbols is not context-dependent.

  3. Context-Freeness: Type 2 grammars lack contextual constraints, meaning that the replacement of symbols does not depend on their context within the string.

  4. Languages: Context-free grammars are widely used in the description of programming languages, syntax analysis, and various computational linguistics applications. Context-free grammars can describe many programming languages.

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