Difference between DFA and NFA

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. DFA NFA
1 DFA stands for Deterministic Finite Automata. NFA stands for Nondeterministic Finite Automata.
2 For 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.
3 DFA cannot use Empty String transition. NFA can use Empty String transition.
4 DFA can be understood as one machine. NFA can be understood as multiple little machines computing at the same time.
5 In DFA, the next possible state is distinctly set. In NFA, each pair of state and input symbol can have many possible next states.
6 DFA is more difficult to construct. NFA is easier to construct.
7 DFA 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.
8 Time needed for executing an input string is less. Time needed for executing an input string is more.
9 All DFA are NFA. Not all NFA are DFA.
10 DFA requires more space. NFA requires less space then DFA.

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