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Deterministic Finite State Automata

Deterministic Finite State Automata. DFA construction and operation. DFA Construction. Input Alphabet : ∑ is finite set of inputs State Set : Q is finite set of states Transition Function : δ : ∑  Q  Q is transition function which takes current input and state and produces next state

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Deterministic Finite State Automata

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  1. Deterministic Finite State Automata DFA construction and operation

  2. DFA Construction • Input Alphabet : ∑ is finite set of inputs • State Set : Q is finite set of states • Transition Function : δ : ∑Q  Q is transition function which takes current input and state and produces next state • Start State : S  Q is start state • Accepting States : F is set of accepting states.

  3. DFA Operation • Given a DFA M and an input string X = x1 x2 . . . Xn • M begins in its start state q0 = S • M produces a state sequence q1 , q2, . . . qn by applying its transition function δ to the next input and current state • where q1 = δ(x1,S) , q2 = δ(x1,q1) , . . . , qn = δ(xn,qn-1) • M accepts string X if qn is in its set of legal final states. Otherwise X is rejected.

  4. Example 2 1 4 3 4

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