This document discusses the differences between non-deterministic finite automata (NFA) and deterministic finite automata (DFA). It states that NFAs can recognize the union, concatenation, and Kleene closure of regular languages. It also notes that any NFA can be converted to an equivalent DFA by constructing transition sets representing the lambda-closures of NFA states. The conversion procedure involves identifying the lambda-closure of each NFA state and making those closures the states of the DFA. Transitions between DFA states are determined by the possible transitions between NFA lambda-closures on given input symbols. This ensures the resulting DFA recognizes the same language as the original NFA.

1. TOCTHEORY OF COMPUTATION
NON-DETERMINISTIC FINITE AUTOMATA V S DETERMINISTIC FINITE AUTOMATA
NFA DFA
Prepared By :-
Avishek Sarkar (130650107020)
Yatish Dhanani (130650107002)
Tej Dave (140650107007)

2. NFA vs. DFA
NFAs can be constructed from DFAs using transitions:
Called NFA-
Suppose M1 accepts L1, M2 accepts L2
Then an NFA can be constructed that accepts:
L1 U L2 (union)
L1L2 (concatenation)
L1
* (Kleene star)

3. Closure Properties of NFA-s
M1
M1
M
M2
M2
L(M1) U L(M2)
L(M1) L(M2)
L(M)*





 

4. Deterministic vs nondeterministic
For every nondeterministic automata, there is an
equivalent deterministic automata
Finite acceptors are equivalent if they both accept the
same language
L(M1) = L(M2)
NFA to DFA Conversion

5. NFA to DFA Conversion
-> In DFA, label resultant state as a set of
states
{q1, q2, q3,…}
For a set of |Q| states, there are exactly 2Q
subsets
Finite number of states

6. Removing Non-deterministic
• By simulating all moves of an NFA-λ in parallel using a DFA.
• λ-closure of a state is the set of states reachable using only
the λ-transitions.

7. NFA-λ
q1
p1
q2
p3
p2
a
λ
λ
λ
p4
a
}5,4,3,2,1{),1( pppppaqt 
p5λ

8. λ – Closure
•Selected λ closures
q1: {q1,q2}
p1: {p1,p2,p3}
q2: {q2}

9. • Given an NFA-λ M1, construct a DFA M2 such that L(M) = L(DM).
• Observe that
• A node of the DFA = Set of nodes of NFA-λ
• Transition of the DFA =
Transition among set of nodes of NFA- λ
Equivalence Construction

10. Start state of DFA =
Final/Accepting state of DFA =
All subsets of states of NFA-λ
that contain an accepting state
of the NFA-λ
})({- 0qclosure
Dead state of DFA = 
Special States to Identify

11. Example
q0
q1
q2
a
a
a
b
λ
c
• Identify λ-closures
• q0: {q0}
• q1: {q1}
• q2: {q1,q2}

12. THANK YOU..!!!