📘 1. Introduction

In Finite Automata (FA), we need a way to represent how states change when input symbols are read.

👉 This is done using:

• Transition Graph (Diagram form)
• Transition Table (Tabular form)

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🧠 2. Transition Graph

✅ Definition

A Transition Graph is a diagrammatic representation of a finite automaton, showing:

• States
• Transitions between states
• Input symbols

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📊 Components of Transition Graph

• Nodes (Circles) → States
• Edges (Arrows) → Transitions
• Labels on edges → Input symbols
• Start State → Arrow pointing to it
• Final State → Double circle

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📌 Example 1: Simple DFA

Language: Strings ending with “ab”

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📊 Transition Graph

→ (q0) --a--> (q1)
(q1) --b--> (q2*)
(q0) --b--> (q0)
(q1) --a--> (q1)
(q2) --a--> (q1)
(q2) --b--> (q0)

• q0 = Start state
• q2 = Final (accepting) state

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🧪 Example Strings

String	Result
ab	✅ Accepted
aab	✅ Accepted
aba	❌ Rejected

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⭐ Key Points (Exam)

👉 Visual representation of FA 👉 Easy to understand behavior 👉 Used for both DFA and NFA

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🧠 3. Transition Table

✅ Definition

A Transition Table is a tabular representation of a finite automaton showing transitions for each state and input.

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📊 Structure

State	Input a	Input b
q0	q1	q0
q1	q1	q2
q2	q1	q0

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📌 Example (Same DFA as Above)

State	a	b
→ q0	q1	q0
q1	q1	q2
*q2	q1	q0

• → = Start state
• • = Final state

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⭐ Key Points (Exam)

👉 Systematic representation 👉 Easy to implement in programs 👉 Used in compiler design

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🔄 4. Transition Function

✅ Definition

A Transition Function (δ) defines how states change.

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📌 Notation

δ(q, a) = next state

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Example

δ(q0, a) = q1
δ(q1, b) = q2

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⚖️ 5. Transition Graph vs Transition Table

Feature	Transition Graph	Transition Table
Form	Diagram	Table
Representation	Visual	Tabular
Understanding	Easy	Moderate
Implementation	Hard	Easy
Use	Design & explanation	Coding & execution

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🔗 6. Conversion Between Graph and Table

🔹 Graph → Table

1. List all states
2. For each input, note next state
3. Fill table

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🔹 Table → Graph

1. Draw states as circles
2. Add arrows based on table
3. Mark start and final states

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🧪 7. Example (Step-by-Step)

Given Transition Table:

State	0	1
→ q0	q1	q0
q1	q1	q2
*q2	q2	q2

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Transition Graph

→ (q0) --0--> (q1)
(q0) --1--> (q0)
(q1) --0--> (q1)
(q1) --1--> (q2*)
(q2) --0--> (q2)
(q2) --1--> (q2)

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⚠️ 8. Errors / Common Mistakes

• Missing transitions
• Incorrect final state marking
• Multiple transitions in DFA (not allowed)

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🎯 9. Important Exam Concepts

👉 Frequently asked:

• Define transition graph
• Define transition table
• Draw DFA using graph
• Convert graph → table
• Convert table → graph
• Define transition function δ

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📝 10. Short Notes (Quick Revision)

• Transition Graph → visual diagram
• Transition Table → tabular form
• Both represent same FA
• δ function defines transitions

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📊 11. Final Summary Table

Aspect	Transition Graph	Transition Table
Definition	Diagram of FA	Table of transitions
Representation	Nodes & edges	Rows & columns
Readability	Easy	Moderate
Implementation	Difficult	Easy
Use	Understanding	Programming
Includes	States, arrows	States, next states
Exam Importance	High	Very High

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✅ Final Conclusion

• Transition Graph helps visualize how automata works
• Transition Table helps implement it efficiently
• Both are equally important in compiler design and exams

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