Is it possible to reverse a pseudo random number generator?
For example, take an array of generated numbers and get the original seed.
If so, how would this be implemented?
This is absolutely possible - you just have to create a PRNG which suits your purposes. It depends on exactly what you need to accomplish - I'd be happy to offer more advice if you describe your situation in more detail.
For general background, here are some resources for inverting a Linear Congruential Generator:
Reversible pseudo-random sequence generator
pseudo random distribution which guarantees all possible permutations of value sequence - C++
And here are some for inverting the mersenne twister:
http://www.randombit.net/bitbashing/2009/07/21/inverting_mt19937_tempering.html
http://b10l.com/reversing-the-mersenne-twister-rng-temper-function/
In general, no. It should be possible for most generators if you have the full array of numbers. If you don't have all of the numbers or know which numbers you have (do you have the 12th or the 300th?), you can't figure it out at all, because you wouldn't know where to stop.
You would have to know the details of the generator. Decoding a linear congruential generator is going to be different from doing so for a counter-based PRNG, which is going to be different from the Mersenne twister, which is going to be different with a Fibonacci generator. Plus you would probably need to know the parameters of the generator. If you had all of that AND the equation to generate a number is invertible, then it is possible. As to how, it really depends on the PRNG.
Use the language Janus a time-reversible language for doing reversible computing.
You could probably do something like create a program that does this (pseudo-code):
x = seed
x = my_Janus_prng(x)
x = reversible_modulus_op(x, N) + offset
Janus has the ability to give to you a program that takes the output number and whatever other data it needs to invert everything, and give you the program that ends with x = seed.
I don't know all the details about Janus or how you could do this, but just thought I would mention it.
Clearly, what you want to do is probably a better idea because if the RNG is not an injective function, then what should it map back to etc.
So you want to write a Janus program that outputs an array. The input to the Janus inverted program would then take an array (ideally).
Related
I have searched for pseudo-RNG algorithms but all I can find seem to generate the next number by using the previous result as seed. Is there a way to generate them non-recursively?
The scenario where I need this is during OpenCL concurrent programming, each thread/pixel needs an independent RNG. I tried to seed them using BIG_NUMBER + work_id, but the result has a strong visual pattern in it. I tried several different RNG algorithms and all have this problem. Apparently they only guarantee the numbers are independent if you generate recursively, but not when you use sequential numbers as seed.
So my question is: Can I generate an array of random numbers, from an array of sequential numbers, independently and constant time for each number? Or is it mathematically impossible?
As the solution to my openCL problem, I can just pre-generate a huge array of random numbers recursively first and store in GPU memory, then use them later using seed as index. But I'm curious about the question above, because it seems very possible just by doing bunch of overflow and cutoffs, according to my very simple understanding of chaos theory.
Can I generate an array of random numbers, from an array of sequential numbers, independently and constant time for each number? Or is it mathematically impossible?
Sure you can - use block cipher in countnig mode. It is generally known as Counter based RNG, first widely used one was Fortuna RNG
I want to generate a sequence of random numbers that will be used to pick tiles for a "maze". Each maze will have an id and I want to use that id as a seed to a pseudo random function. That way I can generate the same maze over and over given it's maze id. Preferably I do not want to use a built in pseudo random function in a language since I do not have control over the algorithm and it could change from platform to platform. As such, I would like to know:
How should I go about implementing my own pseudo random function?
Is it even feasible to generate platform independent pseudo random numbers?
Yes, it is possible.
Here is an example of such an algorithm (and its use) for noise generation.
Those particular random functions (Noise1, Noise2, Noise3, ..) use input parameters and calculate the pseudo random values from there.
Their output range is from 0.0 to 1.0.
And there are many more out there (Like mentioned in the comments).
UPDATE 2019
Looking back at this answer, a better suited choice would be the below-mentioned mersenne twister. Or you could find any implementation of xorshift.
The Mersenne Twister may be a good pick for this. As you can see from the pseudocode on wikipedia, you can seed the RNG with whatever you prefer to produce identical values for any instance with that seed. In your case, the maze ID or the hash of the maze ID.
If you are using Python, you can use the random module by typing at the beginning,
import random. Then, to use it, you type-
var = random.randint(1000, 9999)
This gives the var a 4 digit number that can be used for its id
If you are using another language, there is likely a similar module
I'm not sure StackOverflow is the right place to ask this question, because this question is half-programming and half-mathematics. And also really sorry if my question is stupid ^_^
I'm studying about Monte Carlo simulations via the "Monte Carlo Methods" book. One of the first thing I must learn is about Random Number Generator. The basic algorithm of RNG is:
1. Initialize: Draw the seed S0 from the distribution µ on S. Set t = 1.
2. Transition: Set St = f(St−1).
3. Output: Set Ut = g(St).
4. Repeat: Set t = t+ 1 and return to Step 2.
(µ is a probability distribution on the finite set of states S, the input is S0 and the random number we desire it the output Ut)
It is not hard to understand, but the problem here is I don't see the random factor which lie in the number of repeat. How can we decide when to stop the loop of the RNG? All examples I read which implement a RNG are loop for 100 times, and they returns the same value for a specific seed. It is not random at all >_<
Can someone explain what I'm missing here? Any help will be appreciated. Thanks everyone
You can't get a true sequence of random numbers on a computer, without specialized hardware. (Such specialized hardware performs the equivalent of an initial roll of the dice using physics to provide the randomness. Electronic ones often use the electronic noise of specialized diodes at constant temperatures; others use radioactive decay events.)
Without that specialized hardware, what you can generate are pseudorandom numbers which, as you've observed, always generate the same sequence of numbers for the same initial seed. For simple applications, you can often get away with generating an initial seed from the time of invocation, which is effectively random.
And when I say "simple applications," I am excluding cryptography. (Not just that, but especially that.)
Sometimes when you are trying to debug a simulation, you actually want to have a reproducible stream of "random" numbers so you might specifically sent a stream to start with a specific seed.
For instance in the answer Creating a facet_wrap plot with ggplot2 with different annotations in each plot rcs starts the answer by creating a reproducible set of data using the R code
set.seed(1)
df <- data.frame(x=rnorm(300), y=rnorm(300), cl=gl(3,100)) # create test data
before going on to demonstrate how to answer the actual question.
I'm looking for a determenistic psuedo random generator that takes two inputs and always returns the same output. I'm looking for things like uniform distribution, unpredictable as possible, and doesn't repeat for a long long time. Ideally the function doesn't rely on previous values. The reason that is a problem is I'm generating terrain data for an extremely large procedurely generated world and can't afford to store previous values.
Any help is appreciated.
i think what you're looking for is perlin noise - it's a way of generating "random" values in 2d (typically) that look like terrain / clouds / etc.
note that this doesn't have much to do with cryptography etc, but a "real" random number source is probably not what you want for synthetic terrain (it looks too noisy/spikey).
there's a good article on perlin noise here.
the implementation of perlin noise does use a source of random numbers, but typically you can use whatever is present on your system (starting with a known seed if you want to reproduce it later).
Is the problem deciding on a PRNG algorithm to use or an algorithm that accepts 2 inputs?
If it's the former, why not use the built in random class - such as Random class in .NET - since it strives for uniform distribution and long cycles. Also, given the same seed it will generate the same sequence of numbers.
If it's the latter, what you can do is map the 2 inputs to a single ouput and use that as a seed to your random algorithm. You can define a simple hash function that takes a string and calculates an integer from it:
s[0] + s[1]^1 + s[2]^2 + ... s[n]^n = seed
Combination of two inputs (by concatenating each other, provided the inputs are binary integers) into one seed will do, for a PRNG, such as Mersenne Twister.
I need a random number generation algorithm that generates a random number for a specific input. But it will generate the same number every time it gets the same input. If this kind of algorithm available in the internet or i have to build one. If exists and any one knows that please let me know. (c, c++ , java, c# or any pseudo code will help much)
Thanks in advance.
You may want to look at the built in Java class Random. The description fits what you want.
Usually the standard implementation of random number generator depends on seed value.
You can use standard random with seed value set to some hash function of your input.
C# example:
string input = "Foo";
Random rnd = new Random(input.GetHashCode());
int random = rnd.Next();
I would use a hash function like SHA or MD5, this will generate the same output for a given input every time.
An example to generate a hash in java is here.
The Mersenne Twister algorithm is a good predictable random number generator. There are implementations in most languages.
How about..
public int getRandonNumber()
{
// decided by a roll of a dice. Can't get fairer than that!
return 4;
}
Or did you want a random number each time?
:-)
Some code like this should work for you:
MIN_VALUE + ((MAX_VALUE - MIN_VALUE +1) * RANDOM_INPUT / (MAX_VALUE + 1))
MIN_VALUE - Lower Bound
MAX_VALUE - Upper Bound
RANDOM_INPUT - Input Number
All pseudo-random number generators (which is what most RNGs on computers are) will generate the same sequence of numbers from a starting input, the seed. So you can use whatever RNG is available in your programming language of choice.
Given that you want one sample from a given seed, I'd steer clear of Mersenne Twister and other complex RNGs that have good statistical properties since you don't need it. You could use a simple LCG, or you could use a hash function like MD5. One problem with LCG is that often for a small seed the next value is always in the same region since the modulo doesn't apply, so if your input value is typically small I'd use MD5 for example.