Tag Archives: randomness

Linear time probabilistic pattern matching and the Rabin-Karp algorithm

Output of a multi-patterns string searching algorithmMost linear-time string searching algorithms are tricky to implement, and require heavy preprocessing of the pattern before running the search. This article presents the Rabin-Karp algorithm, a simple probabilistic string searching algorithm based on hashing and polynomial equality testing, along with a Python implementation. A streaming variant of the algorithm and a generalization to searching for multiple patterns in one pass over the input are also described, and performance aspects are discussed.

The algorithm is probabilistic in that it doesn’t always return correct results; more precisely, it returns all valid matches and (with reasonably small probability) a few incorrect matches (algorithms such as this one that tend to be over-optimistic in reporting their results are usually said to be true-biased).

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Modeling and measuring string comparison performance in C, C++, C# and Python.

O(1) Comparing strings is often — erroneously — said to be a costly process. In this article I derive the theoretical asymptotic cost of comparing random strings of arbitrary length, and measure it in C, C++, C# and Python.

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Generating uniformly random data from skewed input: biased coins, loaded dice, skew correction, and the Von Neumann extractor

A spinning coin, about to fall on tailsIn a famous article published 1951, John Von Neumann presented a way of skew-correcting a stream of random digits so as to ensure that 0s and 1s appeared with equal probability. This article introduces a simple and mentally workable generalization of his technique to random dice, so a loaded die can be used to uniformly draw numbers from the set \(\{1, 2, 3, 4, 5, 6\}\), with reasonable success.

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How random is pseudo-random? Testing pseudo-random number generators and measuring randomness

After introducing true and pseudo-random number generators, and presenting the methods used to measure randomness, this article details a number of common statistical tests used to evaluate the quality of random number generators.

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