What are Context-Free Grammars and Backus Naur Form?

Question

Can someone please explain in layman's terms:

1. what a context-free grammar is?

2. what Backus Naur Form is?

3. How to use this notation?

4. How to do string derivation?

5. How to describe language syntax?

Answer 1

A context-free grammar (CFG) G is a quadruple (V, Σ, R, S) where

• V: a set of non-terminal symbols
• Σ: a set of terminals (V ∩ Σ = Ǿ)
• R: a set of rules (R: V → (V U Σ)*)
• S: a start symbol

Example of CFG:

• V = {q, f,}
• Σ = {0, 1}
• R = {q → 11q, q → 00f, f → 11f, f → ε}
• S=q
• (R= {q → 11q | 00f, f → 11f | ε })

As far as I understand, Backus Naur Form (BNF) is another way of representing the things that are shown in the Context-Free Grammar (CFG)

Example of BNF:

[number] ::= [digit] | [number] [digit]

[digit] ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

which can be read as something like: "a number is a digit, or any number followed by an extra digit" (which is a contorted but precise way of saying that a number consists of one or more digits) "a digit is any one of the characters 0, 1, 2, ... 9"

Difference:

Notation of these two representations are a bit different, i-e

--> equals ::=

| equals or

there must be some other differences but to be honest I don't know any other :)

String Derivation:

Let S be the start" symbol

• S --> A, the initial state
• A --> 0A
• A --> 1B
• A --> ?
• B --> 1B
• B --> ?

Example of String Derivation:

Does this grammar generate the string 000111?
yes, it does!

• S --> A
• A --> 0A
• 0A --> 00A
• 00A --> 000A
• 000A --> 0001B
• 0001B --> 00011B
• 00011B --> 000111

that's all from my side, I too am working on it and will surely share if I come to know anymore details about defining the language syntax.

cheers!