Comp Sci Are mixed LCG and combined LCG same thing?

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The discussion centers on the confusion surrounding mixed linear congruential generators (LCGs) and combined LCGs, with participants noting a lack of clear local resources and inconsistent explanations in various texts. It is established that a mixed LCG is essentially an LCG with a non-zero constant term, while a combined LCG refers to a generator that merges multiple LCGs. Participants express frustration over the absence of definitive sources and the differing interpretations found in literature. Ultimately, it is suggested that Wikipedia provides a concise overview that clarifies these concepts. The conversation highlights the need for reliable educational materials on the topic.
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Homework Statement
Linear Congruential Generators
Relevant Equations
Congruence equation
The whole problem arouse because there's no authentic local source. One thing that I need to learn is are these both same thing? Or are different? Is combined LCG also LCG or anything can be called combined method? Even our teachers aren't very sure of it(as they were not the ones who designed this curriculum or know the internal details of the course etc)

Is there any difference between "mixed Linear congruential generator" and "combined linear congruential generator". Are they same thing or different thing?

It's pretty confusing. No 2 books have explained about both topics. No books I've read yet, have talked about both of these.It's getting more confusing as I read more texts about it.
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It says "mixed LCG" or "LCG" are the same thing.
https://www.cse.wustl.edu/~jain/iucee/ftp/k_26rng.pdf
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https://www.eg.bucknell.edu/~xmeng/Course/CS6337/Note/master/node40.html

9ABP6JYsi_FmQxftPf1ItLwVz82_9rpDhl2Te7mdpY220KOKJs.png

Optical Communication with Chaotic Lasers: Applications of Nonlinear Dynamics and Synchronization
x4-DHiRkep2aFvQUKTC5lj_U6l3o_vuSgWdR8i6MD4CDL0x7vQ.png

Monte Carlo Methods in Financial Engineering

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QHG_KNFkx7DJc4vQ22Ke_qtItNrwym73MB1py3dS5LmbHykVzc.png

Jerry Banks
Fezdzb1AkDJrrVIqlcg6CA7Z718DcpCWMNthXNzngqaY7oxvII.png

Molecular Modeling and Simulation: An Interdisciplinary Guide
By Tamar Schlick
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This tells LCG and Mixed LCG is same thing in usage.

PROBABILITY AND STATISTICS - Volume II: Probabilistic Models and Methods ...
edited by Reinhard Viertl

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Encyclopedia of Information Science and Technology, Fifth Edition
edited by Khosrow-Pour D.B.A., Mehdi

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jTcwO6vInOx3f1TLVCsbSH09ACEO7A4ylrTdbGqs7Jt2wwgT6M.png

A Guide to Monte Carlo Simulations in Statistical Physics
By David Landau, Kurt Binder

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Local source
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Local source
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local source

After reading these sources, it feels they're different but my local sources are confusing me. It feels LCGs are specifically just multiplicative and mixed. Whereas, combined Genrators doesn't necessarily named LCG.
 
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I am not going to read all of that, but I think all your questions are qickly answered by Wikipedia: https://en.wikipedia.org/wiki/Linear_congruential_generator

In short
  • A linear congruential generator (LCG) has the form ## x_{n+1} = (a x_n +c) \bmod m ##.
  • A mixed congruential generator is an LCG with ## c \ne 0 ## (edit: presumably because it has a 'mix' of a multiplicative and constant term).
  • A multiplicative congruential generator (aka Lehmer RNG) is an LCC with ## c = 0 ## (edit because it only has a multiplicative term).
  • A "Combined Linear Congruential Generator" is simply a combination of two or more LCGs: one example is the Wichmann Hill generator I see mentioned in one of your references; again wikipedia has more on these: https://en.wikipedia.org/wiki/Combined_linear_congruential_generator
I don't think this is the first time it has turned out that 10 minutes on Wikipedia would have been the best use of your time.
 
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Likes Delta2 and shivajikobardan
Thanks, I'll use wikipedia for confusions like this from now.
 
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