Questions about algorithms that deterministically generate sequences of numbers that have stochastic properties of random sequences.

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What does it mean for a random number generator's sequence to be only 1-dimensionally equidistributed?

Whilst reading up on Xorshift I came across the following (emphases added): The following xorshift+ generator, instead, has 128 bits of state, a maximal period of 2128 − 1[9] and passes BigCrush: ...
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Uniform Random Integer Generation [duplicate]

How can I generate a random integer through calls to a function that generates one random bit at a time. Do I place the bit randomly generated at a random position?
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Are there pseudorandom number generators (PRNG) with no finite period?

The typical and widely used PRNG, the linear congruential generator always has a finite (though possibly "long") period. Are there PRNGs that have no finite period? For this question it is not ...
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proof of convergence in arbitrary precision PRNGs

consider a program that generates a random walk using a PRNG, as in following pseudocode. it uses arbitrary precision arithmetic such that there is no limit on variable values (ie no overflow). ...
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NFA random generator

I'm working on a NFA to DFA conversion tool that is different from the Subset Construction and I need to test this tool. In order to be sure that the immplementation has no bug I'd like to generate a ...
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4answers
229 views

What is a good algorithm for generating random DFAs?

I am generating random DFAs to test a DFA reduction algorithm on them. The algorithm that I'm using right now is as follows: for each state $q$, for each symbol in the alphabet $c$, add $\delta (q, ...
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145 views

Seeding the Mersenne Twister Random Number Generator

I am trying to understand how the Mersenne Twister random number generator works (in particular, the 32-bit TinyMT). I am still relatively new to the concept of RNG. As I read the source code, I ...
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2answers
92 views

Random generator considerations in the design of randomized algorithms

It is well known that the efficiency of randomized algorithms (at least those in BPP and RP) depends on the quality of the random generator used. Perfect random sources are unavailable in practice. ...
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Will the Mersenne Twister PRNG eventually produce all integer sequences of a certain length?

I'm attempting to use the MT19937 variant of the Mersenne Twister PRNG to accomplish something. Whether or not this something is feasible depends upon the answers to these two questions: What is the ...
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Mersenne twister middle word

In some literature, as well as in Wikipedia, the middle term parameter m of Mersenne twister is called "number of parallel sequences". Why? What is meant here by "parallel sequences"?
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2answers
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Rigorous proof against pseudorandom generator

I am trying to teach myself the principles of cryptograhpy, and want to solve the following question: Let G be the algorithm that takes an input x = (x1, . . . , xn) from {0, 1} n (so each xi ∈ ...
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LFSR sequence computation

I need to calculate the output of the sequence generated by this shift register but I cannot find anywhere how to do it. Everywhere the results are just given but there is no explanation how to do ...
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Choosing taps for Linear Feedback Shift Register

I am confused about how taps are chosen for Linear Feedback Shift Registers. I have a diagram which shows a LFSR with connection polynomial $C(X) = X^5 + X^2 + 1$. The five stages are labelled: $R4, ...
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Proving the security of Nisan-Wigderson pseudo-random number generator

Let $\cal{S}=\{S_i\}_{1\leq i\leq n}$ be a partial $(m,k)$-design and $f: \{0,1\}^m \to \{0,1\}$ be a Boolean function. The Nisan-Wigderson generator $G_f: \{0,1\}^l \to \{0,1\}^n$ is defined as ...