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    Mechanism of Howard's algorithm Computer Science

    Mechanism of Howard's algorithm Computer Science


    Mechanism of Howard's algorithm

    Posted: 28 Aug 2021 11:37 AM PDT

    Best Ways to Learn Python

    Posted: 29 Aug 2021 12:33 AM PDT

    The problem of true computational randomness being impossible

    Posted: 19 Aug 2021 08:32 AM PDT

    hello fellow cs enthusiasts,

    I made a video all about computational (pseudo) randomness: https://youtu.be/Kd34K_5YI18

    although it mainly uses python to explain stuff, it really dwells into concepts of pseudo randomness and entropy. i loved researching for this video. it's one of the most favourite videos that I have made. the whole concept was super interesting once you get yourself in the right Mindframe. I would love for you all to check it out and give me feedback regarding it :3

    submitted by /u/OrganizationWinter99
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    Sorting, Information, and Recursion

    Posted: 18 Aug 2021 03:37 PM PDT

    Following up on a previous post in which I proved that a set of numbers is sorted if and only if the distances between adjacent entries in the resultant list are minimized, I've put all the work together in a formal paper with some additional results:

    https://www.researchgate.net/publication/353958877_Sorting_Information_and_Recursion

    The most interesting result is in my opinion that a set is sorted if and only if the amount of information required to encode the set as a particular class of recurrence relations is minimized (see Corollary 3.1).

    This result connects basic computer science (i.e., sorting) to information theory, and function theory, since the type of recursion it's related to is exactly the type you use to define the derivative of a function, which is a finite difference equation.

    Another interesting consequence is a O(N) runtime sorting algorithm (all computations that can be performed independently, are assumed to be performed in parallel), the code for which can be found at the bottom of this post:

    UPDATE:

    There's some confusion in the comments, as the Ω(n log(n)) bounds applies only to sorting in serial. As a result, I've included heavily annotated code in the paper itself, linked to above, that explains the runtime of each step of the algorithms.

    There's an O(N) algorithm (based upon the proof of Theorem 2.1) and another O(log(N)) algorithm that makes use of random noise to solve around the linear steps in the algorithm introduced in the proof.

    submitted by /u/Feynmanfan85
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