Instruct: Given a question, retrieve relevant documents that can help answer the question.
Query: What is the origin of the word "algorithm"?
The word 'algorithm' has its roots in Latinizing the name of Muhammad ibn Musa al-Khwarizmi in a first step to algorismus.[11][12] Al-Khwārizmī (Arabic: الخوارزمي‎, Persian: خوارزمی‎, c. 780–850) was a Persian mathematician, astronomer, geographer, and scholar in the House of Wisdom in Baghdad, whose name means 'the native of Khwarezm', a region that was part of Greater Iran and is now in Uzbekistan.[13][14]
Definition of any normal algorithm consists of two parts: the definition of the "alphabet" algorithm (the algorithm will be applied to words of these alphabet symbols), and the definition of its "scheme". Scheme normal algorithm is a finite ordered set of so-called "substitution formulas", each of which can be "simple" or "final". A simple formula substitutions are called words such as formula_1, where formula_2 and formula_3 – are two arbitrary words in the alphabet of the algorithm (called, respectively, the left and right side of the formula substitution). Similarly, the final substitution formulas are called words of the form formula_4, where formula_2 and formula_3 – are two arbitrary words in the alphabet of the algorithm. This assumes that the auxiliary characters formula_7 and formula_8 do not belong to the alphabet of the algorithm (otherwise an executable their role divider left and right sides should select the other two letters).
The process of applying the normal algorithm to an arbitrary word formula_11 in the alphabet of this algorithm is a discrete sequence of elementary steps, consisting of the following. Let’s assume that formula_12 is the word obtained in the previous step of the algorithm (or the original word formula_11, if the current step is the first). If among formulas of substitution there is no left-hand side of which would be included in the formula_12, then the work of the algorithm is considered completed, and the result of this work is considered to be the word formula_12. Otherwise, including the substitution of the left side of which is included in the formula_12, the very first part is selected. If the substitution formula looks like formula_4, then out of all of possible representations of the word formula_12 that looks like formula_19 it is chosen one formula_20, which is the shortest. Then the work of the algorithm is considered completed with the result formula_21. However, if this substitution formula looks like formula_1, then out of all of possible representations of the word formula_12 in the form of formula_19 it is chosen one, in which formula_20 – the shortest, after which the word formula_21 is considered to be the result of the current step, subject to further processing in the next step.
It is important to realize that the word problem is in fact solvable for many groups "G". For example, polycyclic groups have solvable word problems since the normal form of an arbitrary word in a polycyclic presentation is readily computable; other algorithms for groups may, in suitable circumstances, also solve the word problem, see the Todd–Coxeter algorithm and the Knuth–Bendix completion algorithm. On the other hand the fact that a particular algorithm does not solve the word problem for a particular group does not show that the group has an unsolvable word problem. For instance Dehn's algorithm does not solve the word problem for the fundamental group of the torus. However this group is the direct product of two infinite cyclic groups and so has a solvable word problem.
The most straightforward algorithm is to look for a character match at successive values of the index codice_3, the position in the string being searched, i.e. codice_7. If the index codice_3 reaches the end of the string then there is no match, in which case the search is said to "fail". At each position codice_3 the algorithm first checks for equality of the first character in the word being searched, i.e. codice_10. If a match is found, the algorithm tests the other characters in the word being searched by checking successive values of the word position index, codice_11. The algorithm retrieves the character codice_12 in the word being searched and checks for equality of the expression codice_13. If all successive characters match in codice_1 at position codice_3, then a match is found at that position in the search string.
Tokenization is the process of breaking up a text string into words or other meaningful elements called tokens. Typically, tokenization occurs at the word level. However, it is sometimes difficult to define what is meant by a "word". Often a tokenizer relies on simple heuristics, such as splitting the string on punctuation and whitespace characters. Tokenization is more challenging in languages without spaces between words, such as Chinese and Japanese. Tokenizing text in these languages requires the use of word segmentation algorithms.
A phonetic algorithm is an algorithm for indexing of words by their pronunciation. Most phonetic algorithms were developed for use with the English language; consequently, applying the rules to words in other languages might not give a meaningful result.
While the word "algorithm" goes back only to certain readers of al-Khwārizmī, careful descriptions of methods of solution are older than proofs: such methods (that is, algorithms) are as old as any recognisable mathematics—ancient Egyptian, Babylonian, Vedic, Chinese—whereas proofs appeared only with the Greeks of the classical period.
An interesting early case is that of what we now call the Euclidean algorithm. In its basic form (namely, as an algorithm for computing the greatest common divisor) it appears as Proposition 2 of Book VII in "Elements", together with a proof of correctness. However, in the form that is often used in number theory (namely, as an algorithm for finding integer solutions to an equation formula_78,
or, what is the same, for finding the quantities whose existence is assured by the Chinese remainder theorem) it first appears in the works of Āryabhaṭa (5th–6th century CE) as an algorithm called
"kuṭṭaka" ("pulveriser"), without a proof of correctness.
The package-merge algorithm is an "O(nL)"-time algorithm for finding an optimal length-limited Huffman code for a given distribution on a given alphabet of size "n", where no code word is longer than "L". It is a greedy algorithm, and a generalization of Huffman's original algorithm. Package-merge works by reducing the code construction problem to the binary "coin collector's problem".
A stemming algorithm is the process of taking a word with suffixes and reducing it to its root, or base word. Stemming algorithms are used to improve the accuracy in information retrieval and in domain analysis. These algorithms help find variants of the terms being looked up. Stemming algorithms are helpful because it is likely that users who look up a particular word might be interested in related words. Stemming algorithms are prevalent in search engines, such as Google's, which did not implement word stemming until 2003. This means that up until 2003, a Google search for the word "warm" would not have returned related words like "warmth" or "warming".
The Lesk algorithm is a classical algorithm for word sense disambiguation introduced by Michael E. Lesk in 1986.
The Lesk algorithm is based on the assumption that words in a given "neighborhood" (section of text) will tend to share a common topic. A simplified version of the Lesk algorithm is to compare the dictionary definition of an ambiguous word with the terms contained in its neighborhood. Versions have been adapted to use WordNet. An implementation might look like this:
A machine translation expert, Knight approached language translation as if all languages were ciphers, effectively treating foreign words as symbols for English words. His approach, which tasked an expectation-maximization algorithm with generating every possible match of foreign and English words, enabled the algorithm to figure out a few words with each pass. A comparison with 80 languages confirmed that the original language was likely German, which the researchers had guessed based on the word "Philipp," a German spelling. Knight then used a combination of intuition and computing techniques to decipher most of the code in a few weeks. Megyesi later realized that a particular symbol meant "eye", and Schaefer connected that discovery to the Oculists.
On a phone with a numeric keypad, each time a key (1-9) is pressed (when in a text field), the algorithm returns a guess at what letters are most likely for the keys pressed to that point. For example, to enter the word 'the', one would press 8 then 4 then 3, and the display would display 't' then 'th' then 'the'. If the less common word 'fore' were intended (3673) the predictive algorithm may select 'Ford'. Pressing the 'next' key (typically the '*' key) might bring up 'dose', and finally 'fore'. If 'fore' is selected, then the next time the user presses the sequence 3673, fore would be more likely to be the first word displayed. If the word "Felix" was intended, however, when entering 33549, the display shows 'E', then 'De', 'Del', 'Deli', and 'Felix.' This is an example of a letter changing while entering words.
Hashing is used in database systems as a method to protect sensitive data such as passwords; however it is also used to improve the efficiency of database referencing. Inputted data is manipulated by a hashing algorithm. The hashing algorithm converts the inputted data into a string of fixed length that can then be stored in a database. Hashing systems have two crucially important characteristics that will now be outlined. Firstly, hashes are "unique and repeatable". As an example, running the word "cat" through the same hashing algorithm multiple times will always yield the same hash, however it is extremely difficult to find a word that will return the same hash that "cat" does. Secondly, hashing algorithms are not reversible. To relate this back to the example provided above, it would be nearly impossible to convert the output of the hashing algorithm back to the original input, which was "cat". In the context of database encryption, hashing is often used in password systems. When a user first creates their password it is run through a hashing algorithm and saved as a hash. When the user logs back into the website, the password that they enter is run through the hashing algorithm and is then compared to the stored hash. Given the fact that hashes are unique, if both hashes match then it is said that the user inputted the correct password. One example of a popular hash function is SHA (Secure Hash Algorithm) 256.
A naive decoding algorithm for concatenated codes can not be an optimal way of decoding because it does not take into account the information that maximum likelihood decoding (MLD) gives. In other words, in the naive algorithm, inner received codewords are treated the same regardless of the difference between their hamming distances. Intuitively, the outer decoder should place higher confidence in symbols whose inner encodings are close to the received word. David Forney in 1966 devised a better algorithm called generalized minimum distance (GMD) decoding which makes use of those information better. This method is achieved by measuring confidence of each received codeword, and erasing symbols whose confidence is below a desired value. And GMD decoding algorithm was one of the first examples of soft-decision decoders. We will present three versions of the GMD decoding algorithm. The first two will be randomized algorithms while the last one will be a deterministic algorithm.Consider the received word formula_32 which was corrupted by a noisy channel. The following is the algorithm description for the general case. In this algorithm, we can decode y by just declaring an erasure at every bad position and running the errors and erasure decoding algorithm for formula_17 on the resulting vector.
The original author later produced a new version of the algorithm, which he named Double Metaphone. Contrary to the original algorithm whose application is limited to English only, this version takes into account spelling peculiarities of a number of other languages. In 2009 Lawrence Philips released a third version, called Metaphone 3, which achieves an accuracy of approximately 99% for English words, non-English words familiar to Americans, and first names and family names commonly found in the United States, having been developed according to modern engineering standards against a test harness of prepared correct encodings.
Algorithms have been designed to solve Jumbles, using a dictionary. Common algorithms work by printing all words that can be formed from a set of letters. The solver then chooses the right word.
When the algorithm converges on a stable residual set, a final decision list of the target word is obtained. The most reliable collocations are at the top of the new list instead of the original seed words. The original untagged corpus is then tagged with sense labels and probabilities. The final decision list may now be applied to new data, the collocation with the highest rank in the list is used to classify the new data. For example, if the highest ranking collocation of the target word in the new data set is of sense A, then the target word is classified as sense A.
Minsky (1967) baldly asserts that "an algorithm is "an effective procedure" and declines to use the word "algorithm" further in his text; in fact his index makes it clear what he feels about "Algorithm, "synonym" for Effective procedure"(p. 311):
Simplified LESK Algorithm with smart default word sense (Vasilescu et al., 2004) 
The COMPUTEOVERLAP function returns the number of words in common between two sets, ignoring function words or other words on a stop list. The original Lesk algorithm defines the context in a more complex way.
An XML Signature consists of a codice_1 element in the codice_2 namespace. The basic structure is as follows:When validating an XML Signature, a procedure called Core Validation is followed.This procedure establishes whether the resources were really signed by the alleged party. However, because of the extensibility of the canonicalization and transform methods, the verifying party must also make sure that what was actually signed or digested is really what was present in the original data, in other words, that the algorithms used there can be trusted not to change the meaning of the signed data.
A simple way to do word wrapping is to use a greedy algorithm that puts as many words on a line as possible, then moving on to the next line to do the same until there are no more words left to place. This method is used by many modern word processors, such as OpenOffice.org Writer and Microsoft Word. This algorithm always uses the minimum possible number of lines but may lead to lines of widely varying lengths. The following pseudocode implements this algorithm:
Because of the lack of training data, many word sense disambiguation algorithms use semi-supervised learning, which allows both labeled and unlabeled data. The Yarowsky algorithm was an early example of such an algorithm. It uses the ‘One sense per collocation’ and the ‘One sense per discourse’ properties of human languages for word sense disambiguation. From observation, words tend to exhibit only one sense in most given discourse and in a given collocation.
Consider the problem to be solved by the numerical algorithm as a function  mapping the data  to the solution . The result of the algorithm, say *, will usually deviate from the "true" solution . The main causes of error are round-off error and truncation error. The "forward error" of the algorithm is the difference between the result and the solution; in this case, . The "backward error" is the smallest Δ such that ; in other words, the backward error tells us what problem the algorithm actually solved. The forward and backward error are related by the condition number: the forward error is at most as big in magnitude as the condition number multiplied by the magnitude of the backward error.
Word wrapping is an optimization problem. Depending on what needs to be optimized for, different algorithms are used.