Explain Type-0 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-0 unrestricted grammar

• Type-0 grammars generate recursively enumerable.
• In type-0 the production has no restrictions.
• There may be any phase structure grammar which includes all formal grammars
• They generate the language which is recognized by the Turing machine.
• The productions can be in the form of a->b where, a is a string of terminals and with at least one non-terminals and a cannot be null. b is a string of terminal and non-terminal.

Example

S->ACaB

Bc->acB

CB->DB

aD->Db