Context-free grammars in Compiler Design - Step-by-Step Execution

Concept Flow - Context-free grammars

Start with Start Symbol S

↓

Apply Production Rules

↓

Replace Non-terminals

↓

Generate String of Terminals

↓

Check if String is in Language

Yes No↓

Accept

The grammar starts from a special symbol and applies rules to replace non-terminals until a string of terminals is formed, which is then checked for acceptance.

Execution Sample

Compiler Design

S -> aSb | ε

Generate strings from S

This grammar generates strings with matching numbers of 'a's and 'b's, like 'ab', 'aabb', or the empty string.

Analysis Table

Step	Current String	Action	Resulting String
1	S	Apply S -> aSb	aSb
2	aSb	Apply S -> aSb on middle S	aaSbb
3	aaSbb	Apply S -> ε on middle S	aabb
4	aabb	No non-terminals left	aabb

💡 No non-terminals remain; string 'aabb' generated and accepted.

State Tracker

Variable	Start	After 1	After 2	After 3	Final
Current String	S	aSb	aaSbb	aabb	aabb

Key Insights - 2 Insights

Why do we replace non-terminals step by step instead of all at once?

Replacing non-terminals one at a time (see execution_table steps 1-3) shows how strings grow gradually and helps track derivations clearly.

What does the symbol ε mean in the grammar?

ε means the empty string, so applying S -> ε removes S without adding characters, ending the derivation (see step 3).

Visual Quiz - 3 Questions

Look at the execution_table at step 2, what is the current string?

A aaSbb

B aSb

C aabb

D S

💡 Hint

Check the 'Current String' column at step 2 in the execution_table.

At which step does the grammar replace S with the empty string ε?

A Step 1

B Step 2

C Step 3

D Step 4

💡 Hint

Look for the action mentioning S -> ε in the execution_table.

If we never apply S -> ε, what happens to the string?

A It becomes infinitely long with non-terminals

B It becomes empty immediately

C It becomes a string of only terminals

D It stops at step 4

💡 Hint

Refer to the variable_tracker showing how non-terminals are replaced stepwise.

Concept Snapshot

Context-free grammars start from a start symbol.
They use production rules to replace non-terminals.
Replacements continue until only terminals remain.
The generated strings belong to the language.
ε means empty string, ending replacements.
Used to define programming language syntax.

Full Transcript

Context-free grammars define languages by starting with a special start symbol and applying rules to replace non-terminals with terminals or other non-terminals. This process continues step by step until a string of only terminals is formed. For example, the grammar with rules S -> aSb or S -> ε generates strings with matching numbers of 'a's and 'b's, including the empty string. Each step replaces one non-terminal, showing how the string grows. The empty string rule (ε) allows the derivation to end. This method helps define the syntax of programming languages clearly and precisely.