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Often is a set between 's support and its interior; for instance, if is the uniform distribution on the interval (,], might be (,]. If A {\displaystyle A} is not specified, it is assumed to be some set contained in the support of P {\displaystyle P} and containing its interior, depending on context.
A random seed (or seed state, or just seed) is a number (or vector) used to initialize a pseudorandom number generator.. A pseudorandom number generator's number sequence is completely determined by the seed: thus, if a pseudorandom number generator is later reinitialized with the same seed, it will produce the same sequence of numbers.
In computing, and specifically peer-to-peer file sharing, seeding is the uploading of already downloaded content for others to download from. A peer, a computer that is connected to the network, becomes a seed when having acquired the entire set of data, it begins to offer its upload bandwidth to other peers attempting to download the file.
Noam Nisan (1992) showed that this derandomization can actually be achieved with a pseudorandom generator of seed length () that fools all ()-space machines. Nisan's generator has been used by Saks and Zhou (1999) to show that probabilistic log-space computation can be simulated deterministically in space O ( log 1.5 n ...
Each row shows the state evolving until it repeats. The top row shows a generator with m = 9, a = 2, c = 0, and a seed of 1, which produces a cycle of length 6. The second row is the same generator with a seed of 3, which produces a cycle of length 2. Using a = 4 and c = 1 (bottom row) gives a cycle length of 9 with any seed in [0, 8].
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In a tennis event, one version of seeding is where brackets are set up so that the quarterfinal pairings (barring any upsets) would be the 1 seed vs. the 8 seed, 2 vs. 7, 3 vs. 6 and 4 vs. 5. However, most tennis tournaments follow a different procedure, in which the 1 and 2 seeds are placed in separate brackets, but then the 3 and 4 seeds are ...
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