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

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3
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1answer
46 views

Bias of first values produced by a family of RNGs

Suppose I'm doing a large number of pseudo-random but deterministic experiments, where each experiment requires generating several random numbers. I'm approaching this by having each experiment use a ...
4
votes
1answer
59 views

Period of a pseudo-random sequence generated using an LFSR

I was trying to generate maximal length pseudo random sequence using an linear feedback shift register (LFSR). I have read from many sources that the length of the pseudo random sequence generated ...
1
vote
1answer
27 views

Can a relatively small subset of random numbers be permuted and reused and still guarantee good expected running time for an algorithm like quicksort?

So this is sort of a general question but I'll limit the discussion to randomized quicksort to make it clear. Suppose generating "true" random bits is hard, e.g. because it requires measuring ...
4
votes
1answer
47 views

Distribution of Ones in a Psuedorandom Sequence

Let S be a string in the set (0,1) produced by taking the AND of the output of two maximal length linear feedback shift registers of large period (say 128 bits). It's easy to see from the truth table ...
3
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1answer
28 views

PRNG bad seeding and von Neumann unbiasing

Large period PRNGs such as Mersenne Twister require good seeding otherwise the initial output in the sequence may not seem to be high-quality, at least for the first few words (and in the way that is ...
2
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1answer
97 views

Linear congruential generator with uniform distribution [closed]

I am currently studying linear congruential generators, and there was an example in which I didn't get the code: ...
5
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1answer
63 views

Find missing value in period of LCG

It's well known that linear congruential generators have a full period only if a few properties are fulfilled. Now I need a LCG that does not generate a full period in 2^32 (easy to find, just ...
2
votes
1answer
106 views

A binomial random number generating algorithm that works when $Np$ is very small

I need to generate binomial random numbers: A binomial random number is the number of heads in $N$ tosses of a coin with probability $p$ of a heads on any single toss. If you generate $N$ uniform ...
19
votes
2answers
2k views

Are all pseudo-random number generators ultimately periodic?

Are all pseudo-random number generators ultimately periodic? Or are they periodic at all in the end? By periodic I mean that, like rational numbers, they in the end generate a periodic subsequence... ...
4
votes
1answer
172 views

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 2^128 − 1 and passes BigCrush: ...
2
votes
1answer
99 views

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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1answer
67 views

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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0answers
180 views

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 ...
6
votes
4answers
327 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, ...
1
vote
1answer
317 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 ...
4
votes
2answers
126 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. ...
5
votes
0answers
112 views

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 ...
2
votes
0answers
35 views

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"?
2
votes
2answers
92 views

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 ∈ ...
4
votes
1answer
124 views

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 ...
10
votes
1answer
352 views

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, ...
11
votes
1answer
231 views

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 ...