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# DFA - FiniteAutomata Finite Automata We introduce the...

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1 Finite Automata Finite Automata We introduce the simplest deterministic theoretical machines(DFA): Finite Automata.

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2 Deterministic Finite Automata (DFA) A Deterministic finite automaton (DFA) is the following 3 things: 1. a finite set of states, one of which is designated as the start state , and some (maybe none) of which are designated the final states (or accepting states ) 2. an alphabet Σ of input letters 3. a finite set of transitions that indicate, for each state and letter of the input alphabet, the state to go to next state state letter
3 Finite Automata The language defined or accepted by a finite automaton is the set of words that end in a final state. If w is in the language defined by a finite automaton, then we also say that the finite automaton accepts w.

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4 Finite Automata Example : = {a,b} states = {x,y,z} start state : x final states: {z} a b x y z y x z z z z aaa: a x y a a x y y is not final; aaa is not accepted aaba: a x y a b x z z is final; aaba is accepted z a transitions:
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• Spring '12