Difference between DFA and NFA
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 a single resultant state i.e. there is only one transition. A deterministic finite automata is set of five tuples represented as,
Q: A non-empty finite set of states 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 states in Q.
F: It is a non-empty set of final states/ accepting states from the set belonging to Q.
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 a set of five tuples and represented as,
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.
Prerequisite – Finite Automata
Difference between DFA and NFA :
|DFA stands for Deterministic Finite Automata.
||NFA stands for Nondeterministic Finite Automata.
|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.
|DFA cannot use Empty String transition.
||NFA can use Empty String transition.
|DFA can be understood as one machine.
||NFA can be understood as multiple little machines computing at the same time.
|In DFA, the next possible state is distinctly set.
||In NFA, each pair of state and input symbol can have many possible next states.
|DFA is more difficult to construct.
||NFA is easier to construct.
|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.
|Time needed for executing an input string is less.
||Time needed for executing an input string is more.
|All DFA are NFA.
||Not all NFA are DFA.
|DFA requires more space.
||NFA requires less space then DFA.
Dead configuration is not allowed.
eg: if we give input as 0 on q0 state so we must give 1 as input to q0 as self loop.
Dead configuration is allowed.
eg: if we give input as 0 on q0 state so we can give next input 1 on q1 which will go to next state.
|δ: QxΣ -> Q i.e. next possible state belongs to Q.
||δ: Qx(Σ U ε) -> 2^Q i.e. next possible state belongs to power set of Q.
|Backtracking is allowed in DFA.
||Backtracking is not always possible in NFA.
|Conversion of Regular expression to DFA is difficult.
||Conversion of Regular expression to NFA is simpler compared to DFA.
|Epsilon move is not allowed in DFA
||Epsilon move is allowed in NFA
|DFA allows only one move for single input alphabet.
||There can be choice (more than one move) for single input alphabet.
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