Tags » Computability

Algorithmic Randomness and Complexity

How random is a real? Given two reals, which is more random? How should we even try to quantify these questions, and how do various choices of measurement relate? 105 more words

Mathematics

Failing software - again

The line above is from a real (and current at time-of-posting) job advertisement for a software developer. I’m not positing it because I think it is bad, shocking or dangerous, but mainly because it is illustrative of the real world: developers are expected to be “pragmatic” when it comes to testing the software they make for correctness. 463 more words

Guessing Game & Non-computability

#include <stdio.h>

int main(){
	int n;
	printf("==== Guessing Game ====\n\n");

	printf("RULE:\n");
	printf("1. You guess a number, either 0 or 1.\n");
	printf("2. then I will tell you the correct number.\n\n");

	printf("Please make a guess 0 or 1:\n");
	scanf("%d", &n);
	printf("The correct number is %d.\n", !n);
}
… 66 more words
Math

Not all numbers are computable

When we hear the word number, symbols like 1,,¼, π (area enclosed by a unit circle), ι (symbol for ), ε (infinitesimal),  ω (ordinal infinity), ℵ (cardinal infinity), …. 173 more words

Problem Solving

A Proof Of The Halting Theorem


Toward teaching computability and complexity simultaneously

Large Numbers in Computing source

Wilhelm Ackermann was a mathematician best known for work in constructive aspects of logic. The… 1,007 more words

Proofs

Hector Zenil

I’ve run across some of his work before, but I ran into some new material by Hector Zenil that will likely interest those following information theory, complexity, and computer science here. 482 more words

Information Theory