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Difference between DFA and NFA
Short answer
A DFA has exactly one transition per symbol from each state and no ε-moves, while an NFA may have multiple or zero transitions and can include ε-moves. NFAs are often more compact and easier to design, but DFAs are simpler to implement. Both recognize the same class of regular languages, convertible via the subset construction.
Differentiate between DFA and NFA (NDFA).
Both DFA and NFA accept exactly the regular languages, but they differ in how they move.
| Point | DFA | NFA (NDFA) |
|---|---|---|
| Transition function | δ : Q × Σ → Q | δ : Q × (Σ ∪ {ε}) → 2^Q |
| Moves on a symbol | exactly one next state | zero, one or many next states |
| ε-moves | not allowed | allowed (ε-NFA) |
| Computation | a single path for each input | a tree of paths; accept if some path ends in a final state |
| Dead state | needed to make δ total | missing transitions are allowed (the path simply dies) |
| Acceptance | δ*(q₀, w) ∈ F | δ*(q₀, w) ∩ F ≠ ∅ |
| Design | harder, more states | easier, usually fewer states |
| Implementation | simple and fast, one table lookup per symbol | needs backtracking or tracking a set of states |
| Number of states | n | an NFA with n states may need up to 2ⁿ states as a DFA |
Formal tuple: both are 5-tuples (Q, Σ, δ, q₀, F); only the type of δ differs.
Equivalence. Every NFA can be converted to a DFA by the subset construction, so the two models accept the same class of languages (regular languages).
✓ Answer checked by Claude Opus 5.5 (high effort)
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