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# 04 - Lecture 4 Finite Automata A nite automaton is a...

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Lecture 4: Finite Automata A fnite automaton is a machine (controller) with only a fnite number oF states. It is the simplest and most restricted model oF a com- puter. Such a controller is used in many electromechanical de- vices, e.g., automatic door, liFt, vending machine, wash- ing machine, microwave oven, parts oF digital watches and calculators. Example: vending machine \$2 \$0.5 \$0.5 \$0.5 \$2 \$0.5 \$1 \$1 \$2 \$1 start B C sold A 1

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Deterministic fnite automata Deterministic fnite automata (DFA) : A language recognizer consisting of 1. An input tape — divided into squares, for storing the string input. 2. A fnite control — a controller that can be in a Fnite number of states. 3. A reading head — move one position to the right each step. q 4 q 3 q 2 q 1 q 0 q 5 control Finite bb abaa a b tape Input Reading Head 2
Deterministic fnite automata How does a DFA work? 1. Initialization: The reading head is at the leftmost square. The Fnite control is in the initial state . 2. After reading a symbol, The reading head moves one square to the right. The Fnite control enters a new state, which is deterministically dependent on the current state and current input symbol. 3. After reading the entire input string, If the Fnite control is in a fnal state , the input string is considered accepted . Otherwise, the input string is not . 3

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Deterministic fnite automata A DFA is a quintuple M =( K, Σ ,δ,s,F )where K — a fnite set oF states (oF the machine), Σ — an alphabet (symbols that the machine recog- nizes), s K — the initial state, F K — a set oF fnal states (a.k.a. accepting states) δ
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04 - Lecture 4 Finite Automata A nite automaton is a...

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