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What is the difference between DFA and NFA?
DFA is the short form for the deterministic finite automata and NFA is for the Non-deterministic finite automata. Now, let us understand in detail about these two finite automata.
DFA
A Deterministic Finite automata is a five-tuple automata. Following is the definition of DFA −
M=(Q, Σ, δ,q0,F)
Where,
- Q : Finite set called states.
- Σ : Finite set called alphabets.
- δ : Q × Σ → Q is the transition function.
- q0 ϵ Q is the start or initial state.
- F : Final or accept state.
NFA
NFA also has five states same as DFA, but with different transition function, as shown follows −
δ: Q X Σ → 2Q
Where,
- Q : Finite set of states
- Σ : Finite set of the input symbol
- q0 : Initial state
- F : Final state
- δ : Transition function
Differences
The major differences between the DFA and the NFA are as follows −
| Deterministic Finite Automata | Non-Deterministic Finite Automata |
|---|---|
| Each transition leads to exactly one state called as deterministic | A transition leads to a subset of states i.e. some transitions can be non-deterministic. |
| Accepts input if the last state is in Final | Accepts input if one of the last states is in Final. |
| Backtracking is allowed in DFA. | Backtracking is not always possible. |
| Requires more space. | Requires less space. |
| Empty string transitions are not seen in DFA. | Permits empty string transition. |
| For a given state, on a given input we reach a deterministic and unique state. | For a given state, on a given input we reach more than one state. |
| DFA is a subset of NFA. | Need to convert NFA to DFA in the design of a compiler. |
| δ : Q × Σ → Q For example − δ(q0,a)={q1} | δ : Q × Σ → 2Q For example − δ(q0,a)={q1,q2} |
| DFA is more difficult to construct. | NFA is easier to construct. |
| DFA is understood as one machine. | NFA is understood as multiple small machines computing at the same time. |
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Updated on: 31-Oct-2023
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