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Suffix Automaton
In computer science, a suffix automaton is an efficient data structure for representing the substring index of a given string which allows the storage, processing, and retrieval of compressed information about all its substrings. The suffix automaton of a string S is the smallest directed acyclic graph with a dedicated initial vertex and a set of "final" vertices, such that paths from the initial vertex to final vertices represent the suffixes of the string. In terms of automata theory, a suffix automaton is the minimal partial deterministic finite automaton that recognizes the set of suffixes of a given string S=s_1 s_2 \dots s_n. The state graph of a suffix automaton is called a directed acyclic word graph (DAWG), a term that is also sometimes used for any deterministic acyclic finite state automaton. Suffix automata were introduced in 1983 by a group of scientists from the University of Denver and the University of Colorado Boulder. They suggested a linear time online algo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Substring Index
In computer science, a substring index is a data structure which gives substring search in a text or text collection in sublinear time. If you have a document S of length n, or a set of documents D=\ of total length n, you can locate all occurrences of a pattern P in o(n) time. (See Big O notation.) The phrase full-text index is also often used for an index of all substrings of a text. But is ambiguous, as it is also used for regular word indexes such as inverted files and document retrieval. See full text search. Substring indexes include: * Suffix tree * Suffix array * N-gram index, an inverted file for all N-grams of the text * Compressed suffix arrayR. Grossi and J. S. VitterCompressed Suffix Arrays and Suffix Trees, with Applications to Text Indexing and String Matching ''SIAM Journal on Computing,'' 35(2), 2005, 378-407. * FM-index * LZ-index References {{reflist Algorithms on strings String data structures Database index techniques Substring indices, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Colorado Boulder
The University of Colorado Boulder (CU Boulder, CU, or Colorado) is a public research university in Boulder, Colorado. Founded in 1876, five months before Colorado became a state, it is the flagship university of the University of Colorado system. CU Boulder is a member of the Association of American Universities, a selective group of major research universities in North America, and is classified among R1: Doctoral Universities – Very high research activity. In 2021, the university attracted support of over $634 million for research and spent $536 million on research and development according to the National Science Foundation, ranking it 50th in the nation. The university consists of nine colleges and schools and offers over 150 academic programs, enrolling more than 35,000 students as of January 2022. To date, 5 Nobel Prize laureates, 10 Pulitzer Prize winners, 11 MacArthur "Genius Grant" recipients, 1 Turing Award laureate, and 20 astronauts have been affiliated with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set (mathematics)
A set is the mathematical model for a collection of different things; a set contains '' elements'' or ''members'', which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements. Sets are ubiquitous in modern mathematics. Indeed, set theory, more specifically Zermelo–Fraenkel set theory, has been the standard way to provide rigorous foundations for all branches of mathematics since the first half of the 20th century. History The concept of a set emerged in mathematics at the end of the 19th century. The German word for set, ''Menge'', was coined by Bernard Bolzano in his work ''Paradoxes of the Infinite''. Georg Cantor, one of the founders of set theory, gave the following defin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alphabet (formal Languages)
In formal language theory, an alphabet is a non-empty set of symbol (programming), symbols/glyphs, typically thought of as representing letters, characters, or digits but among other possibilities the "symbols" could also be a set of phonemes (sound units). Alphabets in this technical sense of a set are used in a diverse range of fields including logic, mathematics, computer science, and linguistics. An alphabet may have any cardinality ("size") and depending on its purpose maybe be Finite set, finite (e.g., the alphabet of letters "a" through "z"), countable (e.g., \), or even uncountable (e.g., \). String (computer science), Strings, also known as "words", over an alphabet are defined as a sequence of the symbols from the alphabet set. For example, the alphabet of lowercase letters "a" through "z" can be used to form English words like "iceberg" while the alphabet of both upper and lower case letters can also be used to form proper names like "Wikipedia". A common alphabet is , th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Language Theory
In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of symbols, letters, or tokens that concatenate into strings of the language. Each string concatenated from symbols of this alphabet is called a word, and the words that belong to a particular formal language are sometimes called ''well-formed words'' or ''well-formed formulas''. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar, which consists of its formation rules. In computer science, formal languages are used among others as the basis for defining the grammar of programming languages and formalized versions of subsets of natural languages in which the words of the language represent concepts that are associated with particular meanings or semantics. In computational complexity ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trie
In computer science, a trie, also called digital tree or prefix tree, is a type of ''k''-ary search tree, a tree data structure used for locating specific keys from within a set. These keys are most often strings, with links between nodes defined not by the entire key, but by individual characters. In order to access a key (to recover its value, change it, or remove it), the trie is traversed depth-first, following the links between nodes, which represent each character in the key. Unlike a binary search tree, nodes in the trie do not store their associated key. Instead, a node's position in the trie defines the key with which it is associated. This distributes the value of each key across the data structure, and means that not every node necessarily has an associated value. All the children of a node have a common prefix of the string associated with that parent node, and the root is associated with the empty string. This task of storing data accessible by its prefix can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxime Crochemore
Maxime Crochemore (born 1947) is a French computer scientist known for his numerous contributions to algorithms on strings. He is currently a professor at King's College London. Biography Crochemore earned his doctorate (PhD) in 1978 and his Doctorat d'état (DSc) in 1983 from the University of Rouen. He was a professor at Paris 13 University in 1985–1989, and moved to a professorship at Paris Diderot University in 1989. In 2002–2007, Crochemore was a senior research fellow at King's College London, where he is a professor since 2007. Since 2007, he is also a professor emeritus at the University of Marne-la-Vallée. Crochemore holds an honorary doctorate (2014) from the University of Helsinki. A festschrift in his honour was published in 2009 as a special issue of Theoretical Computer Science. Research contributions Crochemore published over 100 journal papers on string algorithms. He in particular introduced new algorithms for pattern matching, string indexing and text com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anatol Slissenko
Anatol Slissenko (russian: Анатолий Олесьевич Слисенко) (born August 15, 1941) is a Soviet, Russian and French mathematician and computer scientist. Among his research interests one finds automatic theorem proving, recursive analysis, computational complexity, algorithmics, graph grammars, verification, computer algebra, entropy and probabilistic models related to computer science. Early years Anatol Slissenko was born in Siberia, where his father served as head of a regiment of military topography. He graduated from the Leningrad State University, Faculty of Mathematics and Mechanics in 1963 (honors diploma). Academic career He earned his PhD (candidate of sciences, his adviser was Nikolai Aleksandrovich Shanin) in 1967 from the Leningrad Department of Steklov Institute of Mathematics, and his Doctor of Science (higher doctorate) in 1981 from the Steklov Institute of Mathematics in Moscow. During 1963–1981 he was with the Leningrad Depar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anselm Blumer With DAWG
Anselm may refer to: People Saints * Anselm, Duke of Friuli (s), Benedictine monk and abbot Nonantula * Anselm of Canterbury (c. 1033–1109), philosopher, Abbot of Bec, and Archbishop of Canterbury * Anselm of Lucca (1036–1086), better known as Saint Anselm of Lucca Bishops * Anselm I (bishop of Milan) ( 813–818), bishop of Milan * Anselm II (archbishop of Milan) (died 896), also known as Anselm II Capra * Anselm I of Aosta (994–1026), the last bishop to serve as count of Aosta, and brother-in-law of Burchard, bishop of Aosta * Anselm I of Lucca (died 1073), better known as Pope Alexander II * Anselm II (1070s 1090s), bishop of Aosta * Anselm III (archbishop of Milan) ( it, Anselmo da Rho, link=no; 1086–1093) * Anselm IV (archbishop of Milan) ( it, Anselmo da Bovisio, link=no; 1097–1101) * Anselm of Havelberg (–1158), Premonstratensian canon and archbishop of Ravenna * Anselm V (Archbishop of Milan) ( 1126–1136), also known as A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Longest Common Substring Problem
In computer science, the longest common substring problem is to find a longest string that is a substring of two or more strings. The problem may have multiple solutions. Applications include data deduplication and plagiarism detection. Examples The picture shows two strings where the problem has multiple solutions. Although the substring occurrences always overlap, no longer common substring can be obtained by 'uniting' them. The strings "ABABC", "BABCA", and "ABCBA" have only one longest common substring, viz. "ABC" of length 3. Other common substrings are "A", "AB", "B", "BA", "BC" and "C". ABABC , , , BABCA , , , ABCBA Problem definition Given two strings, S of length m and T of length n, find a longest string which is substring of both S and T. A generalization is the k-common substring problem. Given the set of strings S = \, where , S_i, =n_i and \Sigma n_i = N. Find for each 2 \leq k \leq K, a longest string which occurs as substring of at leas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Substring Search
In computer science, string-searching algorithms, sometimes called string-matching algorithms, are an important class of string algorithms that try to find a place where one or several strings (also called patterns) are found within a larger string or text. A basic example of string searching is when the pattern and the searched text are arrays of elements of an alphabet (finite set) Σ. Σ may be a human language alphabet, for example, the letters ''A'' through ''Z'' and other applications may use a ''binary alphabet'' (Σ = ) or a ''DNA alphabet'' (Σ = ) in bioinformatics. In practice, the method of feasible string-search algorithm may be affected by the string encoding. In particular, if a variable-width encoding is in use, then it may be slower to find the ''N''th character, perhaps requiring time proportional to ''N''. This may significantly slow some search algorithms. One of many possible solutions is to search for the sequence of code units instead, but doing so may produ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
