One Sided Error Algorithm
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Las Vegas Algorithm Example
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Monte Carlo Algorithm Example
computer science. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Probabilistic algorithm with two-sided error up vote 2 down vote favorite I am currently studying probabilistic algorithms and came across three major
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complexity classes: BPP: worst-case polynomial time, two-sided error RP: worst-case polynomial time, one-sided error ZPP: average-case polynomial time, no error At first I couldn't understand why one would use an algorithm that could err. I figured it does make sense in some cases though, like primality testing for RSA encryption. The algorithm used there has a one-sided error only, though. Even after hours of thinking about it, I failed to think of an algorithm with two-sided error that actually makes sense and could be / is used in practice. Any pointers would be greatly appreciated. complexity-theory time-complexity probability-theory probabilistic-algorithms share|cite|improve this question asked May 12 '15 at 21:49 Christian Schnorr 1134 Two-sided error seems pretty natural. For example, a court of law could find an innocent person guilty or a guilty person innocent. OK, that's not actually an algorithm but it illustrates the concept. –David Richerby May 12 '15 at 22:05 @DavidRicherby It sure is natural, but I'm looking for
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Las Vegas Algorithm Ppt
is a question and answer site for students, researchers and practitioners of computer science. Join them; it only takes a minute: Sign up Here's how monte carlo algorithm code it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top How does one compute the probability of a false-based Monte Carlo algorithm being correct rigorously? up vote 1 down vote http://cs.stackexchange.com/questions/42486/probabilistic-algorithm-with-two-sided-error favorite Recall that a false-biased Monte Carlo (MC) algorithm is always correct when it returns false for some decision problem i.e. it has a one sided error and its always correct on NO instances. Assume that we have a false-biased MC algorithm. In this case when it says NO its always correct. This means that it is not allowed to say NO on YES instances (otherwise, it would make a mistake). So on YES instances it always says YES (and never NO) and http://cs.stackexchange.com/questions/49006/how-does-one-compute-the-probability-of-a-false-based-monte-carlo-algorithm-bein when it says NO in NO instances, its correct. In other words: So if the answer to some problem is YES, then algorithm $A$ will always output YES, while if the answer is NO, it will output NO with probability at least $\frac{1}{3}$. What confuses me is how one would calculate the probability of the algorithm being correct (say, for only 1 run of it, we can extend it to amplification if we want later). I was told that such an algorithm as described above has probability at least $\frac{1}{3}$ of being correct (i.e. $Pr[\text{correct}] \geq \frac{1}{3}$), however, I wasn't sure how to formally justify this. These are my thought. For calculating the probability of the algorithm being correct I would write down the total law of probability (and Bayes rule)to decide if its correct: $$ Pr[correct] = Pr[correct \mid \text{NO instance} ] P[\text{NO instance}] + Pr[correct \mid \text{YES instance} ] P[\text{YES instance}] $$ $$ Pr[correct] = Pr[A(x) = NO \mid \text{NO instance} ] P[\text{NO instance}] + Pr[A(x) = YES \mid \text{YES instance} ] P[\text{YES instance}] $$ However, it seems that this is not the approach people take when talking about the correctness of an MC algorithm. I understand that in this paradigm of algorithms one does not think of the input as being randomized, so, is the standard thing to say that the probability of getting any instances is 0.5? In that case we have: $$ Pr[correct] = Pr[A(x) = NO \mid \text{NO instance} ] \frac{
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