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

Knowledge and Total Functions

In the article SKETCH OF A PROOF: COMPUTABLE TOTAL FUNCTIONS ARE NOT ENUMERABLE I have used the notion of “total functions”. What is so special about “total functions”? 752 more words

Philosophy