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A 'regime shift' is happening in the Arctic Ocean, scientists say

Scientists at Stanford University have discovered a surprising shift in the Arctic Ocean. Exploding blooms of phytoplankton, the tiny algae at the base of a food web topped by whales and polar bears, have drastically altered ...

Physicists reverse time using quantum computer

Researchers from the Moscow Institute of Physics and Technology teamed up with colleagues from the U.S. and Switzerland and returned the state of a quantum computer a fraction of a second into the past. They also calculated ...

Encryption is less secure than we thought

Information theory—the discipline that gave us digital communication and data compression—also put cryptography on a secure mathematical foundation. Since 1948, when the paper that created information theory first appeared, ...

Discovery could lead to more difficult Sudoku puzzles

( -- A new analysis of number randomness in Sudoku matrices could lead to the development of more difficult and multi-dimensional Sudoku puzzles. In a recent study, mathematicians have found that the way that ...

How algorithms (secretly) run the world

When you browse online for a new pair of shoes, pick a movie to stream on Netflix or apply for a car loan, an algorithm likely has its word to say on the outcome.

Human hearing beats the Fourier uncertainty principle

(—For the first time, physicists have found that humans can discriminate a sound's frequency (related to a note's pitch) and timing (whether a note comes before or after another note) more than 10 times better ...

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In mathematics, computing, linguistics, and related subjects, an algorithm is a finite sequence of instructions, an explicit, step-by-step procedure for solving a problem, often used for calculation and data processing. It is formally a type of effective method in which a list of well-defined instructions for completing a task, will when given an initial state, proceed through a well-defined series of successive states, eventually terminating in an end-state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as probabilistic algorithms, incorporate randomness.

A partial formalization of the concept began with attempts to solve the Entscheidungsproblem (the "decision problem") posed by David Hilbert in 1928. Subsequent formalizations were framed as attempts to define "effective calculability" (Kleene 1943:274) or "effective method" (Rosser 1939:225); those formalizations included the Gödel-Herbrand-Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's "Formulation 1" of 1936, and Alan Turing's Turing machines of 1936–7 and 1939.

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