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.

The Rete algorithm ( or, rarely or ) is an efficient pattern matching algorithm for implementing production rule systems.

The Rete algorithm provides a generalized logical description of an implementation of functionality responsible for matching data tuples (" facts ") against productions (" rules ") in a pattern-matching production system ( a category of rule engine ).

As for conflict resolution, the firing of activated production instances is not a feature of the Rete algorithm.

The Rete algorithm, developed by Charles Forgy, is an example of such a matching algorithm ; it was used in the OPS series of production system languages.

Allen Newell's research group in artificial intelligence had been working on production systems for some time, but Forgy's implementation, based on his Rete algorithm, was especially efficient, sufficiently so that it was possible to scale up to larger problems involving hundreds or thousands of rules.

Dr Charles L. Forgy ( born December 12, 1949 in Texas ) is a computer scientist, known for developing the Rete algorithm used in his OPS5 and other production system languages used to build expert systems.

* Using the source-filter model of speech production through linear prediction ( LP )( see the textbook " speech coding algorithm ");

* Rete algorithm, an efficient pattern matching algorithm for implementing production rule systems

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.

For the algorithm above, one could use the following pseudocode:

* The SEQUEST algorithm for analyzing mass spectra makes use of autocorrelation in conjunction with cross-correlation to score the similarity of an observed spectrum to an idealized spectrum representing a peptide.

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 ).

Bruce Schneier notes that while Blowfish is still in use, he recommends using the more recent Twofish algorithm instead.

In one application, it is actually a benefit: the password-hashing method used in OpenBSD uses an algorithm derived from Blowfish that makes use of the slow key schedule ; the idea is that the extra computational effort required gives protection against dictionary attacks.

Worse yet, since the aforementioned decision problem for CSG's is PSPACE-complete, that makes them totally unworkable for practical use, as a polynomial-time algorithm for a PSPACE-complete problem would imply P = NP.

Church subsequently modified his methods to include use of Herbrand – Gödel recursion and then proved ( 1936 ) that the Entscheidungsproblem is unsolvable: There is no generalized " effective calculation " ( method, algorithm ) that can determine whether or not a formula in either the recursive-or λ-calculus is " valid " ( more precisely: no method to show that a well formed formula has a " normal form ").

Modern methods include the use of lossless data compression for incremental parsing, prediction suffix tree and string searching by factor oracle algorithm ( basically a factor oracle is a finite state automaton constructed in linear time and space in an incremental fashion ).

Yamaha's engineers began adapting Chowning's algorithm for use in a commercial digital synthesizer, adding improvements such as the " key scaling " method to avoid the introduction of distortion that normally occurred in analog systems during frequency modulation, though it would take several years before Yamaha release their FM digital synthesizers.

The earliest surviving description of the Euclidean algorithm is in Euclid's Elements ( c. 300 BC ), making it one of the oldest numerical algorithms still in common use.

The most well-known use of the Cooley – Tukey algorithm is to divide the transform into two pieces of size at each step, and is therefore limited to power-of-two sizes, but any factorization can be used in general ( as was known to both Gauss and Cooley / Tukey ).

For with coprime and, one can use the Prime-Factor ( Good-Thomas ) algorithm ( PFA ), based on the Chinese Remainder Theorem, to factorize the DFT similarly to Cooley – Tukey but without the twiddle factors.

In particular, Winograd also makes use of the PFA as well as an algorithm by Rader for FFTs of prime sizes.

There are many ways in which the flood-fill algorithm can be structured, but they all make use of a queue or stack data structure, explicitly or implicitly.

Adapting the algorithm to use an additional array to store the shape of the region allows generalization to cover " fuzzy " flood filling, where an element can differ by up to a specified threshold from the source symbol.

A process-centric algorithm must necessarily use a stack.

A 4-way floodfill algorithm that use the adjacency technique and a stack as its seed pixel store yields a linear fill with " gaps filled later " behaviour.

Such " partial pivoting " improves the numerical stability of the algorithm ( see also pivot element ); some variants are also in use.

In practical use, this is not a problem, because we are generally only interested in compressing certain types of messages, for example English documents as opposed to jibberish text, or digital photographs rather than noise, and it is unimportant if our compression algorithm makes certain kinds of random sequences larger.

The Gauss algorithm for matrix inversion is probably the oldest solution but this approach does not efficiently use the symmetry of R and r. A faster algorithm is the Levinson recursion proposed by Norman Levinson in 1947, which recursively calculates the solution.

The use of a metasyntactic variable is helpful in freeing a programmer from creating a logically named variable, which is often useful when creating or teaching examples of an algorithm.