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12. DFA - MATH 224 Discrete Mathematics Deterministic...

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8/27/09 11 MATH 224 – Discrete Mathematics Deterministic Finite Automata Finite State Machines Set of States Q Start State q0 … Q Accepting States qf 8 Q Alphabet 8 e.g, {0, 1} Transitions 8 ° (T , qi) ± qj q0 qf1 qf2 q1 q2 q3
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8/27/09 22 MATH 224 – Discrete Mathematics DFA Represented by a Directed Graph Multitasking in an operating System Ready Queue Running Start Blocked Waiting Time slice expired Dequeue d Blocked waiting for a resource, e.g. data from a disk Finished with resource and ready to run
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8/27/09 33 MATH 224 – Discrete Mathematics DFA for Multiples of 3 in binary q0 qf-3 q2 q1 0 1 0 1 0 1 1 Start 0 Example 1 46 remainder 1 string 1 0 1 1 1 0 States 0 1 2 2 2 2 1 Example 2 51 remainder 0 string 1 1 0 0 1 1 States 0 1 3 3 3 1 3
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8/27/09 MATH 224 – Discrete Mathematics DFA for Multiples of 3 in binary including the empty string qf-0 q2 q1 0 1 0 1 1 START 0
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8/27/09 55 MATH 224 – Discrete Mathematics DFA to Recognize Floating Point q0 qf-0 q1 0 - 9 +, 0 - 9 e, E q2 q3 +, 0 - 9 0 - 9 0 - 9 q4 Qf-1 q5 Start 0 - 9 .
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