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Category Math & Algebra

States (comma separated, e.g., q0, q1)

Alphabet (comma separated, e.g., 0, 1)

Start State

Final States

Define NFA Transitions

Enter target states separated by commas (e.g. "q0, q1"). Leave empty for no transition.

DFA Result

DFA States 0

Final States 0

State Mapping Legend

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About

This tool converts a Non-Deterministic Finite Automaton (NFA) into an equivalent Deterministic Finite Automaton (DFA) using the standard Powerset Construction (also known as Subset Construction) algorithm. In Automata Theory, while NFAs are easier to design, DFAs are required for efficient hardware and software implementation.

The converter calculates the transition function δ' for the DFA by tracking the set of all reachable states in the NFA for every input symbol. It automatically handles the Dead State (trap state) and identifies the new set of Final States.

Formulas

The core of the conversion lies in the definition of the DFA transition function δ'. For a subset of NFA states S ⊆ Q and an input symbol a ∈ Σ:

δ'(S, a) = ∪q ∈ S δ(q, a)

A state S in the DFA is an accepting state if and only if it contains at least one accepting state from the NFA:

S ∈ F' ⇔ S ∩ F ≠ NULL

Reference Data

Term	Symbol	Definition
State Set	Q	A finite set of states in the automaton.
Alphabet	Σ	A finite set of input symbols (e.g., {0, 1}).
Transition (NFA)	δ	δ: Q × Σ → P(Q) (Maps to a set of states)
Transition (DFA)	δ'	δ': Q' × Σ → Q' (Maps to a single state)
Start State	q₀	The initial state where computation begins.
Final States	F	The set of accepting states.

Frequently Asked Questions

In a DFA (Deterministic Finite Automaton), for every state and input symbol, there is exactly one next state. In an NFA (Non-Deterministic), there can be zero, one, or multiple next states for the same input.

The DFA constructs states representing sets of NFA states. In the worst case, an NFA with n states can result in a DFA with 2ⁿ states.

This specific tool implements standard NFA-to-DFA conversion. It assumes inputs are consumed on every transition. It does not calculate ε-closures.

If an NFA has no defined transition for a symbol, the process dies. In a DFA, this must be explicit, so we transition to a "Trap" state that loops to itself for all future inputs.