NFA with epsilon

NFA with ∈-Moves

NFA with ∈ moves is exactly same as NFA without ∈ moves. 
But differece exist in the transition function δ. 
δ must include information about ∈ transitions. 

NFA with ∈-Moves has 6 tuples (Q, Σ, δ, q0, F).

Q = finite set of states. 

Σ = finite set input symbols.

δ = transition function that maps Q × (Σ ∪{∈}) to 2Q.

q0 = initial state.

F = set of final states.

The non-deterministic finite automaton can be extended to include the transitions on null/empty input ∈.

For example,
NFA with 

In this NFA with epsilon, 
It accept an input string 'aabc'. 
Or string as number of a's followed by number of b's followed by number of c's. 
The string 'aabc' is accepted by the NFA by following the path with labels a, a, ∈, b, ∈, c.

Transition table for above NFA with ∈NFA's with ∈-transitions are closely related to regular expressions and useful in proving the equivalence between the classes of languages accepted by finite automata and regular expressions.


∈-closure of a state q is a set of states following by all transitions of q that are labeled as ∈.

∈-closure (q0) = (q0, q1, q2) 
∈-closure (q1) = (q1, q2) 
∈-closure (q2) = (q2)

NFA with ∈ to NFA without ∈

NFA with ∈
Transition diagram

Transition table NFA with ∈ 

First find out ∈ closure:
∈-closure (q0) = (q0, q1, q2) 
∈-closure (q1) = (q1, q2) 
∈-closure (q2) = (q2)
Transition table NFA without ∈ 
Python Programming ↓ 👆
Java Programming ↓ 👆
JAVA covered following topics in these notes.
JAVA Programs
Principles of Programming Languages ↓ 👆
Principles of Programming Languages covered following topics in these notes.

Previous years solved papers:
A list of Video lectures References:
  1. Sebesta,”Concept of programming Language”, Pearson Edu 
  2. Louden, “Programming Languages: Principles & Practices” , Cengage Learning 
  3. Tucker, “Programming Languages: Principles and paradigms “, Tata McGraw –Hill. 
  4. E Horowitz, "Programming Languages", 2nd Edition, Addison Wesley

    Computer Organization and Architecture ↓ 👆

    Computer Organization and Architecture covered following topics in these notes.

    1. Structure of desktop computers
    2. Logic gates
    3. Register organization
    4. Bus structure
    5. Addressing modes
    6. Register transfer language
    7. Direct mapping numericals
    8. Register in Assembly Language Programming
    9. Arrays in Assembly Language Programming


    1. William stalling ,“Computer Architecture and Organization” PHI
    2. Morris Mano , “Computer System Organization ”PHI

    Computer Network ↓ 👆
    Computer Network covered following topics in these notes.
    1. Data Link Layer
    2. Framing
    3. Byte count framing method
    4. Flag bytes with byte stuffing framing method
    5. Flag bits with bit stuffing framing method
    6. Physical layer coding violations framing method
    7. Error control in data link layer
    8. Stop and Wait scheme
    9. Sliding Window Protocol
    10. One bit sliding window protocol
    11. A protocol Using Go-Back-N
    12. Selective repeat protocol
    13. Application layer
    1. Andrew S. Tanenbaum, David J. Wetherall, “Computer Networks” Pearson Education.
    2. Douglas E Comer, “Internetworking with TCP/IP Principles, Protocols, And Architecture",Pearson Education
    3. KavehPahlavan, Prashant Krishnamurthy, “Networking Fundamentals”, Wiley Publication.
    4. Ying-Dar Lin, Ren-Hung Hwang, Fred Baker, “Computer Networks: An Open Source Approach”, McGraw Hill.