101
votes
Is von Neumann's randomness in sin quote no longer applicable?
If you're using some hardware source of entropy/randomness, you're not "attempting to generate randomness by deterministic means" (my emphasis). If you're not using any hardware source of entropy/...
- 81.4k
76
votes
Accepted
Is von Neumann's randomness in sin quote no longer applicable?
Just because you can't see a pattern doesn't mean that no pattern exists. Just because a compression algorithm can't find a pattern doesn't mean that no pattern exists. Compression algorithms are ...
D.W.♦
- 156k
49
votes
Can we generate random numbers using irrational numbers like π and e?
For any reasonable definition of perfect, the mechanism you describe is not a perfect random number generator.
Non-repeating isn't enough. The decimal number $0.101001000100001\dots$ is non-repeating ...
- 81.4k
28
votes
Accepted
Simulating a probability of 1 of 2^N with less than N random bits
Wow, great question! Let me try to explain the resolution. It'll take three distinct steps.
The first thing to note is that the entropy is focused more on the average number of bits needed per draw,...
D.W.♦
- 156k
28
votes
Can we generate random numbers using irrational numbers like π and e?
It is cryptographically useless because an adversary can predict every single digit. It is also very time consuming.
- 28.4k
23
votes
Why is the Mersenne Twister regarded as good?
The initial Mersenne-Twister (MT) was regarded as good for some years, until it was found out to be pretty bad with the more advanced TestU01 BigCrush tests and better PRNGs.
This page lists the ...
- 457
21
votes
Is von Neumann's randomness in sin quote no longer applicable?
I've always understood the quote to mean that a deterministic algorithm has a fixed amount of entropy, and although the output can appear "random" it can't contain more entropy than the inputs provide....
- 311
20
votes
Why is the Mersenne Twister regarded as good?
I am the Editor who accepted the MT paper in ACM TOMS back in 1998 and I am also the designer of TestU01. I do not use MT, but mostly MRG32k3a, MRG31k3p, and LRSR113. To know more about these, about ...
- 201
18
votes
Is von Neumann's randomness in sin quote no longer applicable?
Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin.
When you interpret "living in a state of sin" as "doing a nonsense", than it's perfectly ...
- 473
18
votes
Accepted
Can we generate random numbers using irrational numbers like π and e?
The most obvious disadvantage is the unnecessary complexity of PRNG algorithms based on irrational numbers. They require much more computations per generated digit than, say, an LCG; and this ...
- 522
17
votes
Accepted
Problem with the pseudo random number generator One-Time-Pad
You seem to have misunderstood what the key is.
In the context of symmetric encryption, the key is a shared secret: something that is known to both the sender and receiver. For OTP, the key is the ...
- 81.4k
15
votes
Is von Neumann's randomness in sin quote no longer applicable?
I thought I'd chime in on the meaning of "random". Most answers here are talking about the output of random processes, compared to the output of deterministic processes. That's a perfectly good ...
- 602
12
votes
Accepted
Is it possible to simulate a fair coin with a finite number of tossing of a biased one?
No, it's not possible. Suppose the bias of the coin is $1/3$, and suppose you could guarantee termination. Then there would be some $n$ such that this always terminates after $n$ coin flips. Let $S$...
D.W.♦
- 156k
11
votes
Accepted
Why is the Mersenne Twister regarded as good?
A recent paper by Vigna starts with an explanation of the history of Mersenne-Twister (MT), and why it has prevailed so far.
The original paper about the Mersenne Twister was published by Makoto ...
- 228
11
votes
Problem with the pseudo random number generator One-Time-Pad
Now to make a more efficient One-Time-Pad you'd use a pseudo-random number generator
No, no and once again no. I'm concerned that this is what you're being taught. The absolutely fundamental ...
- 1,602
10
votes
Accepted
How best to statistically verify random numbers?
You can't. Randomness is a property of the source, not a property of the values you get from that source. In other words, randomness is a statement about the probability distribution, not about some ...
D.W.♦
- 156k
9
votes
Why is the Mersenne Twister regarded as good?
Somewhat like sorting algorithms in this regard, there is no "one size fits all" PRNG. Different ones are used for different purposes and there is a wide variety of design criteria and uses. It is ...
- 11k
9
votes
Uniform sampling from a simplex
This is to add to the existing answers.
Devroye is an excellent reference for questions of this sort. Chap.7 gives the algorithms needed to generate uniform order statistics, which the OP is after.
...
- 1,489
9
votes
Accepted
Why is randomness a problem? (i.e. why do we care about derandomization?)
Complexity theory is a mathematical theory which aims at addressing one shortcoming of computability theory, namely, it takes into account the use of resources. While it is true that in its early days ...
- 275k
9
votes
Accepted
What makes a pseudorandom generator, a high quality one?
There are several criteria for the quality of a PRNG:
How fast it is. This includes how fast it is to setup it, and how fast it is to produce a single bit (amortized).
How difficult it is to guess ...
- 275k
8
votes
Accepted
Time complexity of this while loop
Worst case, if the second call to rand() returns 0 and the first call doesn't, you get a floating point division by zero, and if you are using standard IEEE 754 arithmetic, the result is +infinity. In ...
- 28.4k
8
votes
Shuffling a list while keeping order relative to related elements
Your problem can be phrased as generating a random linear extension of a partial order. The partial order in your phrase is generated by your constraints. There is a classical algorithm of Matthews ...
- 275k
7
votes
Generate string with large Kolmogrov complexity
No. This is basically Chaitin's incompleteness theorem.
Roughly, the theorem says that there exists a concrete constant $C$ (which is a function of your consistent set of axioms) for which no fixed ...
- 489
7
votes
How to select a binary tree node uniformly at random
The algorithm works just fine.
Note that each node's size field tells you the total number of nodes in the subtree rooted at that node. Throughout this answer, I'm ...
- 81.4k
7
votes
Problem with the pseudo random number generator One-Time-Pad
A pseudorandom generator is a deterministic algorithm, which given a short random seed returns a pseudorandom string fooling certain adversaries (i.e. such adversaries will not be able to distinguish ...
- 13.3k
7
votes
Is von Neumann's randomness in sin quote no longer applicable?
Compression isn't an accurate test of randomness, and nor is looking at an image and saying "that looks random".
Randomness is tested by empirical methods. There are in fact suites of specially ...
- 301
7
votes
Can we generate random numbers using irrational numbers like π and e?
(updated after many people pointed out that random number generator is not the same thing as a single normal sequence)
If you ask whether you can get a normal sequence out of $\pi$ (i.e., all numbers ...
- 1,055
6
votes
Accepted
Should Kolmogorov complexity include all resources or just program size?
Should Kc be restated as being resource based and not solely program size based?
No. If you change the definition like that, you get a different concept, and the different concepts deserves its own ...
D.W.♦
- 156k
6
votes
Are all pseudo-random number generators ultimately periodic?
Simple example of pseudo-random sequence that is not periodic:
concatenate together the binary representations of all positive integers, in order:
...
- 209
6
votes
Accepted
How do incompressible strings and random strings share the same properties?
The theorem says, in effect, that incompressible strings are a deterministic model of random strings. If you have some property that you can prove using random strings, you can also prove it using ...
- 275k
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