Type-3 grammars, Production rules

Regular Grammars

Type-3 Grammars in the Chomsky Hierarchy

What is a Regular Grammar?

A Regular Grammar (Type-3 Grammar) is the most restrictive type in the Chomsky hierarchy. It generates regular languages and has a direct correspondence with finite automata. Regular grammars are fundamental in compiler design and pattern matching.

A Regular Grammar is formally defined as a 4-tuple G = (V, T, P, S) where:

  • V: Finite set of eZz symbols (variables)
  • T: Finite set of terminal symbols (alphabet)
  • P: Finite set of production rules
  • S: Start symbol (S ∈ V)
Types of Regular Grammars:
  • Right-Linear: A → aB or A → a (terminal on left)
  • Left-Linear: A → Ba or A → a (terminal on right)
Chomsky Hierarchy Position: Type-3 (most restrictive) → generates Regular Languages

Example Regular Grammar

Right-linear grammar for binary strings ending with "01"

Grammar G = (V, T, P, S)
  • V = @{S, A, B@}
  • T = @{0, 1@}
  • S = S (start symbol)
Production Rules (P):
S → 0S
S → 1S
S → 0A
A → 1
This grammar generates strings like: 01, 001, 101, 1001, 0101, etc.

String Derivation Process

Example derivation of string "1001" using the grammar:

Step 1: S (start with start symbol)
Step 2: S → 1S (apply production S → 1S)
Step 3: 1S → 10S (apply production S → 0S)
Step 4: 10S → 100A (apply production S → 0A)
Step 5: 100A → 1001 (apply production A → 1)
Final Result: The string "1001" is successfully generated!

Interactive Grammar Builder

Create and test your own regular grammars

Grammar Definition
Grammar Visualization

Build a grammar to see visualization

String Generator

Generate strings using your grammar

String Validator

Test if strings belong to your grammar's language

Grammar to Finite Automaton Converter

Convert your regular grammar to an equivalent finite automaton

Language Analysis

Analyze properties of the language generated by your grammar