Explain Type-1 grammar in TOC

Chomsky Hierarchy represents the class of languages that are accepted by the different machines.

Chomsky hierarchy

Hierarchy of grammars according to Chomsky is explained below as per the grammar types −

Type 0. Unrestricted grammars

   Turing Machine (TM)

Type 1. Context-sensitive grammars

   Linear Bounded Automaton (LBA)

Type 2. Context-free grammars

   Pushdown Automaton (PDA)

Type 3. Regular grammars

   Finite Automaton (FA)

Type-1 Context Sensitive Grammar (CSG)

• Type 1 grammar is also known as context sensitive grammar
• The context sensitive grammar is used to represent context sensitive language

The CSG follows some rules, which are as follows −

• The context sensitive grammar may have more than one symbol on the left hand side of their production rules.
• The number of symbols on the left-hand side must not exceed the number of symbols on the right-hand side.
• The rule of the form A->epsilon is not allowed unless A is a start symbol. It does not occur on the right-hand side of any rule.
• The type 1 grammar has to be in Type-0.
• In type 1 production should be in the form of V->T.
• The count symbol in V is less than or equal to T.

Example

S->AB

AB->abc

B_>b