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# prob_algs - Probabilistic Algorithms Michael Sipser...

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Probabilistic Algorithms Michael Sipser Presented by: Brian Lawnichak

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2 Introduction Probabilistic Algorithm uses the result of a random process “flips a coin” to decide next execution Purpose saves on calculating the actual best choice avoids introducing a bias e.g. query individuals in a large population
3 Probabilistic Turing Machine Definition 10.3 Nondeterministic Turing Machine M each nondeterministic step is a coin flip two legal next moves probability is given to each branch b of M Pr[ b ] = 2 - k where k is the number of coin flips on b

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4 M  on input  w Probability that M accepts input w Pr[ M accepts w ] = Σ Pr[ b ] Probability that M rejects input w Pr[ M rejects w ] = 1 – Pr[ M accepts w ] What if there is a bad coin flip? is this algorithm 100% correct? errors should be accounted for
5 Error Probability  ε Allow the Turing machine an error probability ε where 0 ε < ½ M recognizes language L with error probability ε if w L implies Pr[ M accepts w ] 1 – ε

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