The Alfabeto Unificado para a Escrita do Caboverdiano (Unified Alphabet for Cape Verdean Writing), commonly known as ALUPEC , is the alphabet that was officially recognized by the Cape Verdean government to write Cape Verdean Creole .
66-552: The ALUPEC is a phonetic writing system based on the Latin script and states only which letters should be used to represent each sound. The system does not establish rules for spelling ( orthography ). For that reason, Cape Verdean creole writing is not standardized; the same word or the same sentence may appear written in different ways. Cape Verdeans write idiosyncratically — that is, each person writes in his or her own dialect , sociolect , and idiolect . The descriptive texts concerning
132-595: A binary search algorithm (with cost O ( log n ) {\displaystyle O(\log n)} ) outperforms a sequential search (cost O ( n ) {\displaystyle O(n)} ) when used for table lookups on sorted lists or arrays. The analysis, and study of algorithms is a discipline of computer science . Algorithms are often studied abstractly, without referencing any specific programming language or implementation. Algorithm analysis resembles other mathematical disciplines as it focuses on
198-403: A digraph instead of a single letter), but the "regularity" is retained: there is still an algorithm (but a more complex one) for predicting the spelling from the pronunciation and vice versa. In the second case, true irregularity is introduced, as certain words come to be spelled and pronounced according to different rules from others, and prediction of spelling from pronunciation and vice versa
264-468: A flowchart offers a way to describe and document an algorithm (and a computer program corresponding to it). It has four primary symbols: arrows showing program flow, rectangles (SEQUENCE, GOTO), diamonds (IF-THEN-ELSE), and dots (OR-tie). Sub-structures can "nest" in rectangles, but only if a single exit occurs from the superstructure. It is often important to know how much time, storage, or other cost an algorithm may require. Methods have been developed for
330-526: A morpheme (minimum meaningful unit of language) are often spelt identically or similarly in spite of differences in their pronunciation. That is often for historical reasons; the morphophonemic spelling reflects a previous pronunciation from before historical sound changes that caused the variation in pronunciation of a given morpheme. Such spellings can assist in the recognition of words when reading. Some examples of morphophonemic features in orthography are described below. Korean hangul has changed over
396-506: A computer, Babbage's analytical engine, which is the first device considered a real Turing-complete computer instead of just a calculator . Although a full implementation of Babbage's second device was not realized for decades after her lifetime, Lovelace has been called "history's first programmer". Bell and Newell (1971) write that the Jacquard loom , a precursor to Hollerith cards (punch cards), and "telephone switching technologies" led to
462-680: A computer-executable form, but are also used to define or document algorithms. There are many possible representations and Turing machine programs can be expressed as a sequence of machine tables (see finite-state machine , state-transition table , and control table for more), as flowcharts and drakon-charts (see state diagram for more), as a form of rudimentary machine code or assembly code called "sets of quadruples", and more. Algorithm representations can also be classified into three accepted levels of Turing machine description: high-level description, implementation description, and formal description. A high-level description describes qualities of
528-713: A computing machine or a human who could only carry out specific elementary operations on symbols . Most algorithms are intended to be implemented as computer programs . However, algorithms are also implemented by other means, such as in a biological neural network (for example, the human brain performing arithmetic or an insect looking for food), in an electrical circuit , or a mechanical device. Step-by-step procedures for solving mathematical problems have been recorded since antiquity. This includes in Babylonian mathematics (around 2500 BC), Egyptian mathematics (around 1550 BC), Indian mathematics (around 800 BC and later),
594-405: A different language (the Latin alphabet in these examples) and so does not have single letters available for all the phonemes used in the current language (although some orthographies use devices such as diacritics to increase the number of available letters). Pronunciation and spelling do not always correspond in a predictable way In Bengali, the letters, 'শ', 'ষ', and ' স, correspond to
660-484: A fair degree of accuracy. The phoneme-to-letter correspondence, on the other hand, is often low and a sequence of sounds may have multiple ways of being spelt, often with different meanings. Orthographies such as those of German , Hungarian (mainly phonemic with the exception ly , j representing the same sound, but consonant and vowel length are not always accurate and various spellings reflect etymology, not pronunciation), Portuguese , and modern Greek (written with
726-475: A final ending state. The transition from one state to the next is not necessarily deterministic ; some algorithms, known as randomized algorithms , incorporate random input. Around 825 AD, Persian scientist and polymath Muḥammad ibn Mūsā al-Khwārizmī wrote kitāb al-ḥisāb al-hindī ("Book of Indian computation") and kitab al-jam' wa'l-tafriq al-ḥisāb al-hindī ("Addition and subtraction in Indian arithmetic"). In
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#1732875958781792-499: A high grapheme-to-phoneme correspondence for vowel lengths. Bengali , despite having a slightly shallow orthography, has a deeper orthography than its Indo-Aryan cousins as it features silent consonants at places. Moreover, due to sound mergers, the same phonemes are often represented by different graphemes. On the other hand, Assamese does not have retroflex consonants and so, the characters for retroflex consonants ( like ট ('t') and ড ('d') ) that it has inherited in its script from
858-434: A phonemic orthography such a system would need periodic updating, as has been attempted by various language regulators and proposed by other spelling reformers . Sometimes the pronunciation of a word changes to match its spelling; this is called a spelling pronunciation . This is most common with loanwords, but occasionally occurs in the case of established native words too. In some English personal names and place names,
924-409: A phonemic orthography, allophones will usually be represented by the same grapheme, a purely phonetic script would demand that phonetically distinct allophones be distinguished. To take an example from American English: the /t/ sound in the words "table" and "cat" would, in a phonemic orthography, be written with the same character; however, a strictly phonetic script would make a distinction between
990-525: A programmer can write structured programs using only these instructions; on the other hand "it is also possible, and not too hard, to write badly structured programs in a structured language". Tausworthe augments the three Böhm-Jacopini canonical structures : SEQUENCE, IF-THEN-ELSE, and WHILE-DO, with two more: DO-WHILE and CASE. An additional benefit of a structured program is that it lends itself to proofs of correctness using mathematical induction . By themselves, algorithms are not usually patentable. In
1056-477: A sequence of operations", which would include all computer programs (including programs that do not perform numeric calculations), and any prescribed bureaucratic procedure or cook-book recipe . In general, a program is an algorithm only if it stops eventually —even though infinite loops may sometimes prove desirable. Boolos, Jeffrey & 1974, 1999 define an algorithm to be an explicit set of instructions for determining an output, that can be followed by
1122-416: Is a method or mathematical process for problem-solving and engineering algorithms. The design of algorithms is part of many solution theories, such as divide-and-conquer or dynamic programming within operation research . Techniques for designing and implementing algorithm designs are also called algorithm design patterns, with examples including the template method pattern and the decorator pattern. One of
1188-576: Is a more specific classification of algorithms; an algorithm for such problems may fall into one or more of the general categories described above as well as into one of the following: One of the simplest algorithms finds the largest number in a list of numbers of random order. Finding the solution requires looking at every number in the list. From this follows a simple algorithm, which can be described in plain English as: High-level description: (Quasi-)formal description: Written in prose but much closer to
1254-405: Is also mostly morphophonemic, because it does not reflect vowel reduction, consonant assimilation and final-obstruent devoicing. Also, some consonant combinations have silent consonants. A defective orthography is one that is not capable of representing all the phonemes or phonemic distinctions in a language. An example of such a deficiency in English orthography is the lack of distinction between
1320-490: Is highly non-phonemic. The irregularity of English spelling arises partly because the Great Vowel Shift occurred after the orthography was established; partly because English has acquired a large number of loanwords at different times, retaining their original spelling at varying levels; and partly because the regularisation of the spelling (moving away from the situation in which many different spellings were acceptable for
1386-622: Is no longer possible. Pronunciation and spelling still correspond in a predictable way Examples: sch versus s-ch in Romansch ng versus n + g in Welsh ch versus çh in Manx Gaelic : this is a slightly different case where the same digraph is used for two different single phonemes. ai versus aï in French This is often due to the use of an alphabet that was originally used for
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#17328759587811452-460: Is no truly "correct" recommendation. As an effective method , an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function . Starting from an initial state and initial input (perhaps empty ), the instructions describe a computation that, when executed , proceeds through a finite number of well-defined successive states, eventually producing "output" and terminating at
1518-479: Is that of deep and shallow orthographies , in which the depth of an orthography is the degree to which it diverges from being truly phonemic. The concept can also be applied to nonalphabetic writing systems like syllabaries . In an ideal phonemic orthography, there would be a complete one-to-one correspondence ( bijection ) between the graphemes (letters) and the phonemes of the language, and each phoneme would invariably be represented by its corresponding grapheme. So
1584-499: Is the written language rather than the spoken language, so the phonemes represent the graphemes, and it is unimportant how the word is pronounced. Moreover, the sounds which literate people perceive being heard in a word are significantly influenced by the actual spelling of the word. Sometimes, countries have the written language undergo a spelling reform to realign the writing with the contemporary spoken language. These can range from simple spelling changes and word forms to switching
1650-453: Is useful for uncovering unexpected interactions that affect performance. Benchmarks may be used to compare before/after potential improvements to an algorithm after program optimization. Empirical tests cannot replace formal analysis, though, and are non-trivial to perform fairly. To illustrate the potential improvements possible even in well-established algorithms, a recent significant innovation, relating to FFT algorithms (used heavily in
1716-1094: The Entscheidungsproblem (decision problem) posed by David Hilbert . Later formalizations were framed as attempts to define " effective calculability " or "effective method". 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 1936–37 and 1939. Algorithms can be expressed in many kinds of notation, including natural languages , pseudocode , flowcharts , drakon-charts , programming languages or control tables (processed by interpreters ). Natural language expressions of algorithms tend to be verbose and ambiguous and are rarely used for complex or technical algorithms. Pseudocode, flowcharts, drakon-charts, and control tables are structured expressions of algorithms that avoid common ambiguities of natural language. Programming languages are primarily for expressing algorithms in
1782-481: The Greek alphabet ), as well as Korean hangul , are sometimes considered to be of intermediate depth (for example they include many morphophonemic features, as described above). Similarly to French, it is much easier to infer the pronunciation of a German word from its spelling than vice versa. For example, for speakers who merge /eː/ and /ɛː/, the phoneme /eː/ may be spelt e , ee , eh , ä or äh . English orthography
1848-471: The Hammurabi dynasty c. 1800 – c. 1600 BC , Babylonian clay tablets described algorithms for computing formulas. Algorithms were also used in Babylonian astronomy . Babylonian clay tablets describe and employ algorithmic procedures to compute the time and place of significant astronomical events. Algorithms for arithmetic are also found in ancient Egyptian mathematics , dating back to
1914-567: The Kerala School , and the Brāhmasphuṭasiddhānta . The first cryptographic algorithm for deciphering encrypted code was developed by Al-Kindi , a 9th-century Arab mathematician, in A Manuscript On Deciphering Cryptographic Messages . He gave the first description of cryptanalysis by frequency analysis , the earliest codebreaking algorithm. Bolter credits the invention of the weight-driven clock as "the key invention [of Europe in
1980-740: The Rhind Mathematical Papyrus c. 1550 BC . Algorithms were later used in ancient Hellenistic mathematics . Two examples are the Sieve of Eratosthenes , which was described in the Introduction to Arithmetic by Nicomachus , and the Euclidean algorithm , which was first described in Euclid's Elements ( c. 300 BC ). Examples of ancient Indian mathematics included the Shulba Sutras ,
2046-471: The aspirated "t" in "table", the flap in "butter", the unaspirated "t" in "stop" and the glottalized "t" in "cat" (not all these allophones exist in all English dialects ). In other words, the sound that most English speakers think of as /t/ is really a group of sounds, all pronounced slightly differently depending on where they occur in a word. A perfect phonemic orthography has one letter per group of sounds (phoneme), with different letters only where
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2112-606: The ALUPEC claim that it is "a system composed by 23 letters and four digraphs ". What those texts do not specify is that the ALUPEC also includes the letter Y and the digraph RR . Older documents, such as the 1994 Proposed Criteria of the Unified Alphabet for the Cape Verdean Writing System, showed the following order: A B S D E F G H I J DJ L LH M N NH N̈ O P K R T U V X TX Z Later documents (after 1998) show
2178-521: The ALUPEC was recognized by the Cape Verdean government as a viable system for writing the Cape Verdean Creole, becoming the first (and as of 2023 the only) alphabet to attain such status. Nevertheless, the same law allows the usage of alternative writing models, "as long they are presented in a systematized and scientific way". In 2009, Decree-Law No. 8/2009 officially institutionalized the use of
2244-418: The ALUPEC. In spite of having been officially recognized by the state, the usage of ALUPEC is neither official nor mandatory. Phonemic orthography A phonemic orthography is an orthography (system for writing a language ) in which the graphemes (written symbols) correspond consistently to the language's phonemes (the smallest units of speech that can differentiate words), or more generally to
2310-504: The Ifa Oracle (around 500 BC), Greek mathematics (around 240 BC), Chinese mathematics (around 200 BC and later) , and Arabic mathematics (around 800 AD). The earliest evidence of algorithms is found in ancient Mesopotamian mathematics. A Sumerian clay tablet found in Shuruppak near Baghdad and dated to c. 2500 BC describes the earliest division algorithm . During
2376-458: The Japanese hiragana and katakana syllabaries (and the different treatment in English orthography of words derived from Latin and Greek). Alphabetic orthographies often have features that are morphophonemic rather than purely phonemic. This means that the spelling reflects to some extent the underlying morphological structure of the words, not only their pronunciation. Hence different forms of
2442-470: The Middle Ages ]," specifically the verge escapement mechanism producing the tick and tock of a mechanical clock. "The accurate automatic machine" led immediately to "mechanical automata " in the 13th century and "computational machines"—the difference and analytical engines of Charles Babbage and Ada Lovelace in the mid-19th century. Lovelace designed the first algorithm intended for processing on
2508-578: The United States, a claim consisting solely of simple manipulations of abstract concepts, numbers, or signals does not constitute "processes" (USPTO 2006), so algorithms are not patentable (as in Gottschalk v. Benson ). However practical applications of algorithms are sometimes patentable. For example, in Diamond v. Diehr , the application of a simple feedback algorithm to aid in the curing of synthetic rubber
2574-450: The algorithm itself, ignoring how it is implemented on the Turing machine. An implementation description describes the general manner in which the machine moves its head and stores data in order to carry out the algorithm, but does not give exact states. In the most detail, a formal description gives the exact state table and list of transitions of the Turing machine. The graphical aid called
2640-588: The algorithm's properties, not implementation. Pseudocode is typical for analysis as it is a simple and general representation. Most algorithms are implemented on particular hardware/software platforms and their algorithmic efficiency is tested using real code. The efficiency of a particular algorithm may be insignificant for many "one-off" problems but it may be critical for algorithms designed for fast interactive, commercial or long life scientific usage. Scaling from small n to large n frequently exposes inefficient algorithms that are otherwise benign. Empirical testing
2706-592: The alphabet proposed by the Colóquio Linguístico de Mindelo , in 1979. On 20 July 1998, the ALUPEC was approved by the Conselho de Ministros de Cabo Verde , for a five-year trial period. According to the same council, the ALUPEC would "take into account the diversity of the Cape Verdean Language in all the islands, and only after that trial period its introduction in schools would be considered". In 2005,
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2772-403: The analysis of algorithms to obtain such quantitative answers (estimates); for example, an algorithm that adds up the elements of a list of n numbers would have a time requirement of O ( n ) {\displaystyle O(n)} , using big O notation . The algorithm only needs to remember two values: the sum of all the elements so far, and its current position in
2838-679: The ancient Brahmi script are also pronounced like their dental versions. Moreover, in both Bengali and Assamese do not make any distinctions in vowel length. Thus the letters like ই ('i') and ঈ ('i:') as well as উ ('u') and ঊ ('u:') have the same pronunciations as 'i' and 'u' respectively. This leads to the existence of many homophones (words with same pronunciations but different spellings and meanings) in these languages. French , with its silent letters and its heavy use of nasal vowels and elision , may seem to lack much correspondence between spelling and pronunciation, but its rules on pronunciation, though complex, are consistent and predictable with
2904-473: The centuries from a highly phonemic to a largely morphophonemic orthography. Japanese kana are almost completely phonemic but have a few morphophonemic aspects, notably in the use of ぢ di and づ du (rather than じ ji and ず zu , their pronunciation in standard Tokyo dialect ), when the character is a voicing of an underlying ち or つ. That is from the rendaku sound change combined with the yotsugana merger of formally different morae. The Russian orthography
2970-413: The code execution through various routes (referred to as automated decision-making ) and deduce valid inferences (referred to as automated reasoning ). In contrast, a heuristic is an approach to solving problems that do not have well-defined correct or optimal results. For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there
3036-459: The development of the first computers. By the mid-19th century, the telegraph , the precursor of the telephone, was in use throughout the world. By the late 19th century, the ticker tape ( c. 1870s ) was in use, as were Hollerith cards (c. 1890). Then came the teleprinter ( c. 1910 ) with its punched-paper use of Baudot code on tape. Telephone-switching networks of electromechanical relays were invented in 1835. These led to
3102-517: The early 12th century, Latin translations of said al-Khwarizmi texts involving the Hindu–Arabic numeral system and arithmetic appeared, for example Liber Alghoarismi de practica arismetrice , attributed to John of Seville , and Liber Algorismi de numero Indorum , attributed to Adelard of Bath . Hereby, alghoarismi or algorismi is the Latinization of Al-Khwarizmi's name; the text starts with
3168-763: The entire writing system itself, as when Turkey switched from the Arabic alphabet to the Latin -based Turkish alphabet . Methods for phonetic transcription such as the International Phonetic Alphabet (IPA) aim to describe pronunciation in a standard form. They are often used to solve ambiguities in the spelling of written language. They may also be used to write languages with no previous written form. Systems like IPA can be used for phonemic representation or for showing more detailed phonetic information (see Narrow vs. broad transcription ). Phonemic orthographies are different from phonetic transcription; whereas in
3234-427: The field of image processing), can decrease processing time up to 1,000 times for applications like medical imaging. In general, speed improvements depend on special properties of the problem, which are very common in practical applications. Speedups of this magnitude enable computing devices that make extensive use of image processing (like digital cameras and medical equipment) to consume less power. Algorithm design
3300-417: The following order: A B D DJ E F G H I J K L LH M N NH N̈ O P R S T TX U V X Z The ALUPEC comes close to a perfect phonetic system in that almost every letter represents only one sound and almost every sound is represented by only one letter. The vowels may have a graphic accent, but the system does not consider letters with accents as separate letters. Additional notes: The ALUPEC emerged in 1994, from
3366-450: The input list. If the space required to store the input numbers is not counted, it has a space requirement of O ( 1 ) {\displaystyle O(1)} , otherwise O ( n ) {\displaystyle O(n)} is required. Different algorithms may complete the same task with a different set of instructions in less or more time, space, or ' effort ' than others. For example,
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#17328759587813432-482: The invention of the digital adding device by George Stibitz in 1937. While working in Bell Laboratories, he observed the "burdensome" use of mechanical calculators with gears. "He went home one evening in 1937 intending to test his idea... When the tinkering was over, Stibitz had constructed a binary adding device". In 1928, a partial formalization of the modern concept of algorithms began with attempts to solve
3498-514: The language's diaphonemes . Natural languages rarely have perfectly phonemic orthographies; a high degree of grapheme–phoneme correspondence can be expected in orthographies based on alphabetic writing systems, but they differ in how complete this correspondence is. English orthography , for example, is alphabetic but highly nonphonemic. In less formally precise terms, a language with a highly phonemic orthography may be described as having regular spelling or phonetic spelling . Another terminology
3564-627: The most important aspects of algorithm design is resource (run-time, memory usage) efficiency; the big O notation is used to describe e.g., an algorithm's run-time growth as the size of its input increases. Per the Church–Turing thesis , any algorithm can be computed by any Turing complete model. Turing completeness only requires four instruction types—conditional GOTO, unconditional GOTO, assignment, HALT. However, Kemeny and Kurtz observe that, while "undisciplined" use of unconditional GOTOs and conditional IF-THEN GOTOs can result in " spaghetti code ",
3630-641: The page Defective script § Latin script . The graphemes b and v represent the same phoneme in all varieties of Spanish (except in Valencia), while in the Spanish of the Americas, /s/ can be represented by graphemes s , c , or z . Modern Indo-Aryan languages like Hindi , Punjabi , Gujarati , Maithili and several others feature schwa deletion , where the implicit default vowel is suppressed without being explicitly marked as such. Others, like Marathi , do not have
3696-552: The phrase Dixit Algorismi , or "Thus spoke Al-Khwarizmi". Around 1230, the English word algorism is attested and then by Chaucer in 1391, English adopted the French term. In the 15th century, under the influence of the Greek word ἀριθμός ( arithmos , "number"; cf. "arithmetic"), the Latin word was altered to algorithmus . One informal definition is "a set of rules that precisely defines
3762-419: The relationship between the spelling of the name and its pronunciation is so distant that associations between phonemes and graphemes cannot be readily identified. Moreover, in many other words, the pronunciation has subsequently evolved from a fixed spelling, so that it has to be said that the phonemes represent the graphemes rather than vice versa. And in much technical jargon, the primary medium of communication
3828-526: The same sound / ʃ /. Moreover, consonant clusters , 'স্ব', 'স্য' , 'শ্ব ', 'শ্ম', 'শ্য', 'ষ্ম ', 'ষ্য', also often have the same pronunciation, / ʃ / or / ʃ ʃ /. Most orthographies do not reflect the changes in pronunciation known as sandhi in which pronunciation is affected by adjacent sounds in neighboring words (written Sanskrit and other Indian languages , however, reflect such changes). A language may also use different sets of symbols or different rules for distinct sets of vocabulary items such as
3894-552: The same word) happened arbitrarily over a period without any central plan. However even English has general, albeit complex, rules that predict pronunciation from spelling, and several of these rules are successful most of the time; rules to predict spelling from the pronunciation have a higher failure rate. Most constructed languages such as Esperanto and Lojban have mostly phonemic orthographies. The syllabary systems of Japanese ( hiragana and katakana ) are examples of almost perfectly shallow orthography – exceptions include
3960-508: The sounds distinguish words (so "bed" is spelled differently from "bet"). A narrow phonetic transcription represents phones , the sounds humans are capable of producing, many of which will often be grouped together as a single phoneme in any given natural language, though the groupings vary across languages. English, for example, does not distinguish between aspirated and unaspirated consonants, but other languages, like Korean , Bengali and Hindi do. The sounds of speech of all languages of
4026-450: The spelling of a word would unambiguously and transparently indicate its pronunciation, and conversely, a speaker knowing the pronunciation of a word would be able to infer its spelling without any doubt. That ideal situation is rare but exists in a few languages. There are two distinct types of deviation from the phonemic ideal. In the first case, the exact one-to-one correspondence may be lost (for example, some phoneme may be represented by
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#17328759587814092-645: The tested orthographies, Chinese and French orthographies, followed by English and Russian, are the most opaque regarding writing (i.e. phonemes to graphemes direction) and English, followed by Dutch, is the most opaque regarding reading (i.e. graphemes to phonemes direction); Esperanto, Arabic, Finnish, Korean, Serbo-Croatian and Turkish are very shallow both to read and to write; Italian is shallow to read and very shallow to write, Breton, German, Portuguese and Spanish are shallow to read and to write. With time, pronunciations change and spellings become out of date, as has happened to English and French . In order to maintain
4158-422: The use of ぢ and づ ( discussed above ) and the use of は, を, and へ to represent the sounds わ, お, and え, as relics of historical kana usage . There is also no indication of pitch accent, which results in homography of words like 箸 and 橋 (はし in hiragana), which are distinguished in speech. Xavier Marjou uses an artificial neural network to rank 17 orthographies according to their level of Orthographic depth . Among
4224-488: The voiced and voiceless "th" phonemes ( / ð / and / θ / , respectively), occurring in words like this / ˈ ð ɪ s / (voiced) and thin / ˈ θ ɪ n / (voiceless) respectively, with both written ⟨th⟩ . Languages whose current orthographies have a high grapheme-to-phoneme and phoneme-to-grapheme correspondence (excluding exceptions due to loan words and assimilation) include: Many otherwise phonemic orthographies are slightly defective, see
4290-565: The world can be written by a rather small universal phonetic alphabet. A standard for this is the International Phonetic Alphabet . Algorithm In mathematics and computer science , an algorithm ( / ˈ æ l ɡ ə r ɪ ð əm / ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation . Algorithms are used as specifications for performing calculations and data processing . More advanced algorithms can use conditionals to divert
4356-449: Was deemed patentable. The patenting of software is controversial, and there are criticized patents involving algorithms, especially data compression algorithms, such as Unisys 's LZW patent . Additionally, some cryptographic algorithms have export restrictions (see export of cryptography ). Another way of classifying algorithms is by their design methodology or paradigm . Some common paradigms are: For optimization problems there
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