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Difference between DFA and NFA
  • Difficulty Level : Easy
  • Last Updated : 26 Feb, 2021

Prerequisite – Finite Automata 

1. DFA : 
DFA refers to Deterministic Finite Automaton. A Finite Automata(FA) is said to be deterministic, if corresponding to an input symbol, there is single resultant state i.e. there is only one transition. 
A deterministic finite automata is set of five tuples and represented as, 

 

Where, 
Q: A non empty finite set of states present in the finite control(qo, q1, q2, …). 
Σ: A non empty finite set of input symbols. 
δ: It is a transition function that takes two arguments, a state and an input symbol, it returns a single state. 
qo: It is starting state, one of the state in Q. 
F: It is non-empty set of final states/ accepting states from the set belonging to Q. 



2. NFA : 
NFA refers to Nondeterministic Finite Automaton. A Finite Automata(FA) is said to be non deterministic, if there is more than one possible transition from one state on the same input symbol. 
A non deterministic finite automata is also set of five tuples and represented as, 

 

Where, 
Q: A set of non empty finite states. 
Σ: A set of non empty finite input symbols. 
δ: It is a transition function that takes a state from Q and an input symbol from and returns a subset of Q. 
qo: Initial state of NFA and member of Q. 
F: A non-empty set of final states and member of Q. 

Difference between DFA and NFA : 

 

SR.NO.DFANFA
1DFA stands for Deterministic Finite Automata.NFA stands for Nondeterministic Finite Automata.
2For each symbolic representation of the alphabet, there is only one state transition in DFA.No need to specify how does the NFA react according to some symbol.
3DFA cannot use Empty String transition.NFA can use Empty String transition.
4DFA can be understood as one machine.NFA can be understood as multiple little machines computing at the same time.
5In DFA, the next possible state is distinctly set.In NFA, each pair of state and input symbol can have many possible next states.
6DFA is more difficult to construct.NFA is easier to construct.
7DFA rejects the string in case it terminates in a state that is different from the accepting state.NFA rejects the string in the event of all branches dying or refusing the string.
8Time needed for executing an input string is less.Time needed for executing an input string is more.
9All DFA are NFA.Not all NFA are DFA.
10DFA requires more space.NFA requires less space then DFA.
11.Dead state may be required.Dead state is not required.
12.δ: QxΣ -> Q i.e. next possible state belongs to Q.δ: QxΣ -> 2^Q i.e. next possible state belongs to power set of Q.

 

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