He was highly influential in the development of computer science, giving a formalisation of the concepts of " algorithm " and " computation " with the Turing machine, which can be considered a model of a general purpose computer.

In 2002, a theoretical attack, termed the " XSL attack ", was announced by Nicolas Courtois and Josef Pieprzyk, purporting to show a weakness in the AES algorithm due to its simple description .< ref >

ALGOL ( short for ALGOrithmic Language ) is a family of imperative computer programming languages originally developed in the mid 1950s which greatly influenced many other languages and was the standard method for algorithm description used by the ACM, in textbooks, and academic works for the next 30 years and more.

He also was the original author of rzip, which uses a similar algorithm to rsync.

In 1929, Mojżesz Presburger showed that the theory of natural numbers with addition and equality ( now called Presburger arithmetic in his honor ) is decidable and gave an algorithm that could determine if a given sentence in the language was true or false.

Image showing shock waves from NASA's X-43A hypersonic research vehicle in flight at Mach 7, generated using a computational fluid dynamics algorithm. On September 30, 1935 an exclusive conference was held in Rome with the topic of high velocity flight and the possibility of breaking the sound barrier.

A notable example was Phil Katz's PKARC ( and later PKZIP, using the same ". zip " algorithm that WinZip and other popular archivers now use ); also other concepts of software distribution like freeware, postcardware like JPEGview and donationware like Red Ryder for the Macintosh first appeared on BBS sites.

But the study of these curves was first developed in 1959 by mathematician Paul de Casteljau using de Casteljau's algorithm, a numerically stable method to evaluate Bézier curves.

The basic search procedure was proposed in two seminal papers in the early 60s ( see references below ) and is now commonly referred to as the Davis – Putnam – Logemann – Loveland algorithm (" DPLL " or " DLL ").

Huffman coding is the most known algorithm for deriving prefix codes, so prefix codes are also widely referred to as " Huffman codes ", even when the code was not produced by a Huffman algorithm.

A simple Internet search finds millions of sequences in HTML pages for which the algorithm to replace an ampersand by the corresponding character entity reference was probably applied repeatedly.

As of 2002, an asymmetric key length of 1024 bits was generally considered the minimum necessary for the RSA encryption algorithm.

It was then analyzed by researchers in the company, and signal processing expert John Platt designed an improved version of the algorithm.

What amounts to an algorithm for solving this problem was described by Aryabhata ( 6th century ; see ).

Developed in the early 1970s at IBM and based on an earlier design by Horst Feistel, the algorithm was submitted to the National Bureau of Standards ( NBS ) following the agency's invitation to propose a candidate for the protection of sensitive, unclassified electronic government data.

This time, IBM submitted a candidate which was deemed acceptable — a cipher developed during the period 1973 – 1974 based on an earlier algorithm, Horst Feistel's Lucifer cipher.

The suspicion was that the algorithm had been covertly weakened by the intelligence agency so that they — but no-one else — could easily read encrypted messages.

Another theoretical attack, linear cryptanalysis, was published in 1994, but it was a brute force attack in 1998 that demonstrated that DES could be attacked very practically, and highlighted the need for a replacement algorithm.

Now there was an algorithm to study.

It was noted by Biham and Shamir that DES is surprisingly resistant to differential cryptanalysis, in the sense that even small modifications to the algorithm would make it much more susceptible.

A divide and conquer algorithm for triangulations in two dimensions is due to Lee and Schachter which was improved by Guibas and Stolfi and later by Dwyer.

The original algorithm was described only for natural numbers and geometric lengths ( real numbers ), but the algorithm was generalized in the 19th century to other types of numbers, such as Gaussian integers and polynomials in one variable.

For a particularly robust two-pass algorithm for computing the variance, first compute and subtract an estimate of the mean, and then use this algorithm on the residuals.

The first approach is to compute the statistical moments by separating the data into bins and then computing the moments from the geometry of the resulting histogram, which effectively becomes a one-pass algorithm for higher moments.

A more numerically stable two-pass algorithm first computes the sample means, and then the covariance:

Even greater accuracy can be achieved by first computing the means, then using the stable one-pass algorithm on the residuals.

The complexity of executing an algorithm with a human-assisted Turing machine is given by a pair, where the first element represents the complexity of the human's part and the second element is the complexity of the machine's part.

A common misconception is to use inverse order of encryption as decryption algorithm ( i. e. first XORing P17 and P18 to the ciphertext block, then using the P-entries in reverse order ).

If a " weak " character is followed by another " weak " character, the algorithm will look at the first neighbouring " strong " character.

Ada Lovelace created the first algorithm designed for processing by a computer and is usually recognized as history's first computer programmer.

A real number is called computable if there is an algorithm which, given n, returns the first n digits of the number.

The proof of this fact relies on an algorithm which, given the first n digits of Ω, solves Turing's halting problem for programs of length up to n. Since the halting problem is undecidable, Ω can not be computed.

Given the first n digits of Ω and a k ≤ n, the algorithm enumerates the domain of F until enough elements of the domain have been found so that the probability they represent is within 2 < sup >-( k + 1 )</ sup > of Ω.

As mentioned above, the first n bits of Gregory Chaitin's constant Omega are random or incompressible in the sense that we cannot compute them by a halting algorithm with fewer than n-O ( 1 ) bits.

So there is a short non-halting algorithm whose output converges ( after finite time ) onto the first n bits of Omega.

In other words, the enumerable first n bits of Omega are highly compressible in the sense that they are limit-computable by a very short algorithm ; they are not random with respect to the set of enumerating algorithms.

If a is smaller than b, the first step of the algorithm swaps the numbers.

: This formula is often used to compute least common multiples: one first computes the gcd with Euclid's algorithm and then divides the product of the given numbers by their gcd.

It was used to compute the first 206, 158, 430, 000 decimal digits of π on September 18 to 20, 1999, and the results were checked with Borwein's algorithm.

The first part of the algorithm computes an LU decomposition, while the second part writes the original matrix as the product of a uniquely determined invertible matrix and a uniquely determined reduced row-echelon matrix.

This result is a system of linear equations in triangular form, and so the first part of the algorithm is complete.

Some systems cannot be reduced to triangular form, yet still have at least one valid solution: for example, if y had not occurred in and after the first step above, the algorithm would have been unable to reduce the system to triangular form.