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Unformatted text preview: Probabilistic Algorithms Michael Sipser Presented by: Brian Lawnichak 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 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...
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This note was uploaded on 07/25/2008 for the course CSE 860 taught by Professor Chung during the Spring '04 term at Michigan State University.
 Spring '04
 CHUNG
 Algorithms

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