Deterministic Finite Automata (DFA) A DFA is a formal model for recognizing and processing sequences of characters. A DFA is a finite machine with a finite...
Deterministic Finite Automata (DFA)
A DFA is a formal model for recognizing and processing sequences of characters. A DFA is a finite machine with a finite number of states, each represented by a distinct symbol.
A DFA has a start state and a set of transitions from each state to other states. A DFA also has a set of final states, which represent the strings that the DFA can recognize.
A DFA is deterministic if each transition takes the DFA from a given state to a unique state, regardless of the history of the DFA.
Example:
Consider a DFA that recognizes the language of all strings of even length. The DFA would have 2 states, a start state and an accepting state. There would be a transition from the start state to the accepting state for any string that is even in length.
Formal Definition:
A DFA is a tuple <Q, Σ, δ, q_start, F>, where:
Q is the set of states of the DFA.
Σ is the alphabet of the DFA.
δ is the transition function, which maps each state and string to a new state.
q_start is the start state.
F is the set of final states.
Properties of DFAs:
A DFA is finite if and only if it has a finite number of states.
A DFA is deterministic if and only if every transition takes the DFA from a given state to a unique state.
A DFA is regular if every string in the language of the DFA is recognized by the DFA