Questions tagged [randomness]
Randomness is a way to mathematically model uncertainty. We often assume to have access to some well-defined source of random numbers, or that input values or events follow some probability distribution.
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Please help me with exercise 6.3.3 of László Lovász Computational Complexity lecture notes
Let us call a Boolean formula with n variables simple if it is
either unsatisiable or has at least 2^n / n^2 satisfying assignments. Give a probabilistic polynomial algorithm to decide the ...
3
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1answer
47 views
Random observations of a total ordering, how much they tell us?
Suppose we have a total ordering over elements $a_1,a_2, ..., a_n$, meaning there is permutation $\pi$ such that $a_{\pi(1)}<a_{\pi(2)}<...<a_{\pi(n)}$. But we don't know $\pi$. What we know ...
1
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1answer
32 views
Uniformly random iteration of subtrees
I want to iterate through the first $k$ elements of a randomly ordered list containing all subtrees for a given tree. The definition of subtrees that I'm using is: "A subtree of $T$ is a subgraph of $...
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1answer
34 views
PRNG for a gaussian distribution?
I need suggestions for algorithm for Pseudo random number generators that will produce a near gaussian distribution (bell curve) for automatically generating test data. I know that PRNG produce ...
2
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1answer
28 views
Sublinear Homomorphism Property Testing Counter Example
This is a homework question, so I'm not looking for answers, just general guidance.
I'm looking at a Sublinear Algorithms survey where (Group) Homomorphism property testing is discussed. The case of ...
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1answer
20 views
Concentration bound for sum of dependent geometric random variable?
consider following persudocode:
i=0
while(i< k):
uniformly pick u,v in V
if(uv in E):
remove uv form E;
i++;
let $T$ be the number of ...
1
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0answers
25 views
Matrix with zero spectral radius
I need an algorithm which generates a random matrix with spectral radius equal zero.
The only solution I have so far is to generate two vectors $v,w$, normal onto each other ($v\perp w$), and then ...
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1answer
70 views
Is there a name for this shuffle algorithm?
Is there a standard name for the following algorithm? At each step, the code picks an index, remove the object at that index, and remember to never pick that index again. See the following ...
0
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2answers
30 views
Random conditional association
I have a really specific problem to solve and i'm looking for an existing algorithm to help me (i hope i'm in the right section of stackExchange).
I would have to make "random" association between ...
1
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1answer
27 views
On uniform randomness of the weight of the remaining edges of a graph after deleting some of them
Suppose we have a graph $G(V,E,W)$, where $V$ and $E$ are the set of vertices and edges and $W$ is non-negative weight on the edges. Let $w(e)$ be the weight of edge $e$ and $N(e)$ be the neighboring ...
0
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0answers
61 views
If P=BPP, then Is it correct that IP=NP?
I'm now studying Interactive Proof System in Goldreich's textbook and here. I have the following question:
Suppose P=BPP, then this show that randomness doesn't give us power over deterministic ...
5
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1answer
115 views
Is it possible to simulate a fair coin with a finite number of tossing of a biased one?
It is a classic problem to simulate a fair coin with a biased one.
According to Fair Coin (wiki),
John von Neumann gave the following procedure:
Toss the coin twice.
If the results ...
1
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2answers
127 views
How to determine seed collision probability in a PRNG?
I want to use a PRNG to generate random patterns. I would provide the PRNG with a hash value as a seed. Ideally, the seed size would be 64-bit or 128-bit and I would expect no collisions if the seeds ...
2
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1answer
26 views
Is there a complexity class “BQP without error”?
I was wondering if there is a complexity class for problems that can be solved efficiently by a quantum computer such that it always gives the right answer? For example the Deutsch-Josza algorithm ...
1
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0answers
74 views
Generate higher dimensional pink noise
1D Pink noise, is easy enough to generate. See https://www.dsprelated.com/showarticle/908.php for example.
What about higher-dimensional pink noise, such as 2D or 3D pink noise? Is there an algorithm ...
3
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1answer
88 views
How could you characterize “true randomness” of a finite sequence?
This question occurred to me while reading http://arxiv.org/abs/1806.08762/ Any observed sequence is necessarily finite, and any finite sequence is computable, either by explicitly storing all the ...
0
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1answer
57 views
Finding the Entropy of a random experiment with probability of $\frac{1}{3}$
Entropy is the randomness collected by an operating system or application for use in Cryptography or other uses that require random data. The formula for Entropy is $$H(p_1, ..., p_k)=-\sum_{i=1}^{k} ...
2
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1answer
196 views
Generating uniformly random bits from a stream of arbitrarily biased bits
Say we have a function called GenBiasedBit. This function returns 1 with probability p (where p is an unknown real number between 0 and 1 exclusive) and returns 0 with probability 1 − p. How could I ...
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11answers
9k views
Is von Neumann's randomness in sin quote no longer applicable?
Some chap said the following:
Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin.
That's always taken to mean that you can't generate ...
1
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1answer
53 views
Are there any stochastic models of non determinism in the rate of program execution?
We know that typical operating systems and high level languages (especially those with garbage collection) cannot be used for real time operating systems. Java & jet engines don't mix, and ...
1
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2answers
53 views
Would using mouse position in the below scenario generate true random numbers?
I'm having trouble wrapping my head around random number generation so I figure it would be better to ask now, rather than screw up later.
Let's say I want to write a function that generates a random ...
7
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3answers
2k views
Problem with the pseudo random number generator One-Time-Pad
I've started learning cryptography in class and we've come across One-Time-Pads, in which the key (uniformally agreed upon) is as long as the message itself. Then you turn the message into bits, do $...
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1answer
63 views
Placing small circles randomly inside a larger circle, where no two small circles intersect
Sorry if this is the wrong place to ask, was unsure...let me know if it belongs some where else.
So i am trying to work out a way to write an algorithm to place a series of small circles of a set ...
2
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1answer
67 views
Why doesn't this put $BPP$ in $NP$?
From Sipser Gacs we know $x\in L(M)$ for a machine $M\in BPP$ $\iff$ $$\exists t_1,\dots,t_{|r|}\forall r\in\{0,1\}^{|r|}\vee_{i\in\{1,\dots,|r|\}}M(x,r\oplus t_i)=1.$$
From Adleman we know $x\in L(M)...
3
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1answer
49 views
RNG: removing bias by counting bits
I have a hardware RNG that sends me some random bits. Due to nature of that RNG, the source is biased. Then, the bitstream is processed in a following way to remove the bias:
two counters are used, ...
2
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1answer
112 views
Expected Linear time Minimum Spanning Tree algorithm
I am trying to understand the proposed "Randomized Linear-Time Algorithm to Find MST".
My findings:
I have read and search almost every available resource( main paper, wiki, reports on paper, lecture ...
0
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1answer
36 views
Looping through random integers - will it halt with probability 1?
Say I have a simple program that has the pseudocode like this:
...
1
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1answer
36 views
Randomly choose a line - algorithm
We have a large file that can't fit into internal memory. How do we randomly pick one line so that each line has the same probability to be picked?
And how do we randomly pick such n lines so that ...
4
votes
3answers
1k views
How to select a binary tree node uniformly at random
The exercise I'm trying to solve is
You are implementing a binary search tree class from scratch, which, in addition, to insert, find and delete, has a method ...
3
votes
2answers
47 views
Indexing a random permutation
I am curious if there exists a method for specifying a permutation $F_k: X \to X$ with a small(ish) $k$.
Something that comes very close to my goal is a block cipher, say AES. But block ciphers have ...
3
votes
2answers
277 views
What Good Is Kolmogorov Complexity Since It Is Relative?
Kolmogorov complexity is relative to a choice of Universal Turing Machine. Because of the Invariance Theorem, the difference in complexity assigned by two Universal Turing Machines is bounded by a ...
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1answer
93 views
Fitness model for scale free networks
In order to generate scale-free networks, we can use this algorithm, derived from Barabási–Albert model:
1) we assign every node a "weight" $\theta_i$ (or two in the direct case).
2) we place $m$ ...
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3answers
82 views
Given a sufficiently powerful computer and model, can dice rolls be predicted?
I guess that this is a chaos, randomness and modelling question. Can it be conceived that a sufficiently powerful (perhaps quantum) computer might be able to accurately predict the scores on a ...
1
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0answers
37 views
What is the relationship between entropy rate and quantization?
I have a totally random source of signal data that looks like a typical normal distribution. I've included an image as I like pictures:-
The source has a mean of 0, and a standard deviation of 1. ...
0
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1answer
32 views
TRNG by hamming distance of processor tics
I hardly remember on a lecture, where it was told, that the distance of the practical actual running-speed of a processor to the previous tic is used, to generated a true random entropy for seeding. ...
7
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2answers
167 views
What makes a pseudorandom generator, a high quality one?
Reading this answer to this SO question: Why do we not combine random number generators?, it talks about
very high-quality PRNG (Pseudo Random Number Generator)
so it makes me wonder what ...
2
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1answer
517 views
How to understand the analysis of expected running time of randomized quick-sort in this paper?
I'm learning the book named Data Structures & Algorithms in Python.
On Page 557-558, there is a proof of the expected running time of randomized qucick-sort. I have some problems confusing me ...
5
votes
2answers
308 views
Shuffling a list while keeping order relative to related elements
I'm looking to shuffle a list of the elements $a_1,\dots, a_6, \dots, e_1, \dots, e_6$
while keeping two rules:
if I loop though the list and filter out a specific letter or number it should be in ...
2
votes
3answers
357 views
Why do we need Gibbs sampling (and MCMC)?
I just learned about Gibbs Sampling which is an MCMC method. Given a distribution $\pi$, we want to sample an item according to $\pi$.
Maybe my alternative suggestion would sound somewhat naive (even ...
0
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1answer
41 views
Difference in scale between mean page loading times and exponentially distributed page loading times?
Apologies if this is the wrong place to ask.
For my experiment, I have a single-page application and a multi-page application. I am testing them with an exponential distributed delay throttling. The ...
0
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2answers
1k views
Algorithm to create tournament brackets
I'm designing a web app to host e-sports tournaments and want to create an algorithm that generates tournament brackets.
Given a list of participants' user ID's (minimum 4, maximum let's say 64), I ...
2
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3answers
2k views
Time complexity of this while loop
So, i would like to know the time complexity of the following codes:
...
0
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0answers
19 views
Generating symmetric keys
Let's assume that we have to generate huge number of 256-bit symmetric keys. How to do it and how to be sure that it is safe. Perhaps it requires a strong mathematical backend. Don't hesitate to ...
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0answers
22 views
Are exponential random graph models based on Maximum Entropy Principle?
Can anyone shed light on whether or not ERGMs are network models based on the maximum entropy principle? Especially if we say that the available information about the network is in the form of network ...
0
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3answers
188 views
What is the time complexity of this аlgorithm? O(n * r)
Given function rand7 returns random integer in interval [0, 6]. Your task is to implement function ...
4
votes
1answer
39 views
Given a Noisy Curve, Write a Function to Output Likely Slopes
I am training a Variational Autoencoder (type of convolutional neural network), and have been plotting cost over time. The result is a noisy curve, shown here:
I would like to write a function that ...
1
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1answer
58 views
Random function “returns a uniformly distributed int”. Does this mean the probability of every number is the same?
Most functions that generate random numbers are described as:
Returns a pseudorandom, uniformly distributed int value between 0
(inclusive) and the specified value (exclusive)
If I use it to ...
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0answers
29 views
Generation of 11 bit random number
I need camera to sign one random line(there are something like 2000 lines) from the frame each second.
At the beginning I have some 64 bits seed with high entropy from physical RNG and a secure ...
0
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1answer
41 views
How to find a good saw function for PRNG?
As part of an assignment I have to write a PRNG using a sin (or any other trigonometric function) and a saw function which I'm struggling a bit with. So how would you find a good saw function with ...
2
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1answer
126 views
Can Von Neumann bit extraction be made more efficient?
I want to develop a previous question regarding Von Neumann debiasing /randomness extraction.
The typical solution (as posted) is to take pairs of throws and output a bit based on a comparison of ...
