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pseudorandom generator (Definition)

Let $ G$ be a deterministic polynomial-time function from $ \mathbb{N}^{<\omega}$ to $ \mathbb{N}^{<\omega}$ with stretch function $ l:\mathbb{N}\rightarrow\mathbb{N}$, so that if $ x$ has length $ n$ then $ G(x)$ has length $ l(n)$. Then let $ G_n$ be the distribution on strings of length $ l(n)$ defined by the output of $ G$ on a randomly selected string of length $ n$ selected by the uniform distribution.

Then we say $ G$ is pseudorandom generator if $ \{G_n\}_{n\in\mathbb{N}}$ is pseudorandom.

In effect, $ G$ translates a random input of length $ n$ to a pseudorandom output of length $ l(n)$. Assuming $ l(n)>n$, this expands a random sequence (and can be applied multiple times, since $ G_n$ can be replaced by the distribution of $ G(G(x))$).



"pseudorandom generator" is owned by Henry.
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Also defines:  stretch function
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Cross-references: multiple, sequence, expands, translates, pseudorandom, uniform distribution, strings, distribution, length, function, polynomial-time
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This is version 3 of pseudorandom generator, born on 2002-09-15, modified 2005-02-14.
Object id is 3460, canonical name is PsuedorandomGenerator.
Accessed 3105 times total.

Classification:
AMS MSC: 68Q30 (Computer science :: Theory of computing :: Algorithmic information theory )
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