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Levenshtein Automaton
In computer science, a Levenshtein automaton for a string ''w'' and a number ''n'' is a finite-state automaton that can recognize the set of all strings whose Levenshtein distance from ''w'' is at most ''n''. That is, a string ''x'' is in the formal language recognized by the Levenshtein automaton if and only if ''x'' can be transformed into ''w'' by at most ''n'' single-character insertions, deletions, and substitutions. Applications Levenshtein automata may be used for spelling correction, by finding words in a given dictionary that are close to a misspelled word. In this application, once a word is identified as being misspelled, its Levenshtein automaton may be constructed, and then applied to all of the words in the dictionary to determine which ones are close to the misspelled word. If the dictionary is stored in compressed form as a trie, the time for this algorithm (after the automaton has been constructed) is proportional to the number of nodes in the trie, significantly f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Backtracking
Backtracking is a class of algorithms for finding solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons a candidate ("backtracks") as soon as it determines that the candidate cannot possibly be completed to a valid solution. The classic textbook example of the use of backtracking is the eight queens puzzle, that asks for all arrangements of eight chess queens on a standard chessboard so that no queen attacks any other. In the common backtracking approach, the partial candidates are arrangements of ''k'' queens in the first ''k'' rows of the board, all in different rows and columns. Any partial solution that contains two mutually attacking queens can be abandoned. Backtracking can be applied only for problems which admit the concept of a "partial candidate solution" and a relatively quick test of whether it can possibly be completed to a valid solution. It is useless, for example, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
TRE (computing)
TRE is an open-source library for pattern matching in text, which works like a regular expression engine with the ability to do approximate string matching. It was developed by Ville Laurikari and is distributed under a 2-clause BSD-like license. The library is written in C and provides functions which allow using regular expressions for searching over input text lines. The main difference from other regular expression engines is that TRE can match text fragments in an approximate way, that is, supposing that text could have some number of typos. Features TRE uses extended regular expression syntax with the addition of "directions" for matching preceding fragment in approximate way. Each of such directions specifies how many typos are allowed for this fragment. Approximate matching is performed in a way similar to Levenshtein distance, which means that there are three types of typos 'recognized': TRE allows specifying of ''cost'' for each of three typos type independently. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Agrep
agrep (approximate grep) is an open-source approximate string matching program, developed by Udi Manber and Sun Wu between 1988 and 1991, for use with the Unix operating system. It was later ported to OS/2, DOS, and Windows. It selects the best-suited algorithm for the current query from a variety of the known fastest (built-in) string searching algorithms, including Manber and Wu's bitap algorithm based on Levenshtein distances. agrep is also the search engine in the indexer program GLIMPSE. agrep is under a free ISC License. Alternative implementations A more recent agrep is the command-line tool provided with the TRE regular expression library. TRE agrep is more powerful than Wu-Manber agrep since it allows weights and total costs to be assigned separately to individual groups in the pattern. It can also handle Unicode. Unlike Wu-Manber agrep, TRE agrep is licensed under a 2-clause BSD-like license. FREJ (Fuzzy Regular Expressions for Java) open-source library provides comm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite State Transducer
A finite-state transducer (FST) is a finite-state machine with two memory ''tapes'', following the terminology for Turing machines: an input tape and an output tape. This contrasts with an ordinary finite-state automaton, which has a single tape. An FST is a type of finite-state automaton (FSA) that maps between two sets of symbols. An FST is more general than an FSA. An FSA defines a formal language by defining a set of accepted strings, while an FST defines relations between sets of strings. An FST will read a set of strings on the input tape and generates a set of relations on the output tape. An FST can be thought of as a translator or relater between strings in a set. In morphological parsing, an example would be inputting a string of letters into the FST, the FST would then output a string of morphemes. Overview An automaton can be said to ''recognize'' a string if we view the content of its tape as input. In other words, the automaton computes a function that maps ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Damerau–Levenshtein Distance
In information theory and computer science, the Damerau–Levenshtein distance (named after Frederick J. Damerau and Vladimir I. Levenshtein.) is a string metric for measuring the edit distance between two sequences. Informally, the Damerau–Levenshtein distance between two words is the minimum number of operations (consisting of insertions, deletions or substitutions of a single character, or transposition of two adjacent characters) required to change one word into the other. The Damerau–Levenshtein distance differs from the classical Levenshtein distance by including transpositions among its allowable operations in addition to the three classical single-character edit operations (insertions, deletions and substitutions). In his seminal paper, Damerau stated that in an investigation of spelling errors for an information-retrieval system, more than 80% were a result of a single error of one of the four types. Damerau's paper considered only misspellings that could be correct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Full-text Search
In text retrieval, full-text search refers to techniques for searching a single computer-stored document or a collection in a full-text database. Full-text search is distinguished from searches based on metadata or on parts of the original texts represented in databases (such as titles, abstracts, selected sections, or bibliographical references). In a full-text search, a search engine examines all of the words in every stored document as it tries to match search criteria (for example, text specified by a user). Full-text-searching techniques became common in online bibliographic databases in the 1990s. Many websites and application programs (such as word processing software) provide full-text-search capabilities. Some web search engines, such as AltaVista, employ full-text-search techniques, while others index only a portion of the web pages examined by their indexing systems. Indexing When dealing with a small number of documents, it is possible for the full-text-search engine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apache Lucene
Apache Lucene is a free and open-source search engine software library, originally written in Java by Doug Cutting. It is supported by the Apache Software Foundation and is released under the Apache Software License. Lucene is widely used as a standard foundation for non-research search applications. Lucene has been ported to other programming languages including Object Pascal, Perl, C#, C++, Python, Ruby and PHP. History Doug Cutting originally wrote Lucene in 1999. Lucene was his fifth search engine, having previously written two while at Xerox PARC, one at Apple, and a fourth at Excite. It was initially available for download from its home at the SourceForge web site. It joined the Apache Software Foundation's Jakarta family of open-source Java products in September 2001 and became its own top-level Apache project in February 2005. The name Lucene is Doug Cutting's wife's middle name and her maternal grandmother's first name. Lucene formerly included a number of sub-pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Product
In mathematics, specifically set theory, the Cartesian product of two sets ''A'' and ''B'', denoted ''A''×''B'', is the set of all ordered pairs where ''a'' is in ''A'' and ''b'' is in ''B''. In terms of set-builder notation, that is : A\times B = \. A table can be created by taking the Cartesian product of a set of rows and a set of columns. If the Cartesian product is taken, the cells of the table contain ordered pairs of the form . One can similarly define the Cartesian product of ''n'' sets, also known as an ''n''-fold Cartesian product, which can be represented by an ''n''-dimensional array, where each element is an ''n''-tuple. An ordered pair is a 2-tuple or couple. More generally still, one can define the Cartesian product of an indexed family of sets. The Cartesian product is named after René Descartes, whose formulation of analytic geometry gave rise to the concept, which is further generalized in terms of direct product. Examples A deck of cards An ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String (computer Science)
In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable. The latter may allow its elements to be mutated and the length changed, or it may be fixed (after creation). A string is generally considered as a data type and is often implemented as an array data structure of bytes (or words) that stores a sequence of elements, typically characters, using some character encoding. ''String'' may also denote more general arrays or other sequence (or list) data types and structures. Depending on the programming language and precise data type used, a variable declared to be a string may either cause storage in memory to be statically allocated for a predetermined maximum length or employ dynamic allocation to allow it to hold a variable number of elements. When a string appears literally in source code, it is known as a string literal or an anonymous string. In formal languages, which are used in mathematical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Language
In theoretical computer science and formal language theory, a regular language (also called a rational language) is a formal language that can be defined by a regular expression, in the strict sense in theoretical computer science (as opposed to many modern regular expressions engines, which are augmented with features that allow recognition of non-regular languages). Alternatively, a regular language can be defined as a language recognized by a finite automaton. The equivalence of regular expressions and finite automata is known as Kleene's theorem (after American mathematician Stephen Cole Kleene). In the Chomsky hierarchy, regular languages are the languages generated by Type-3 grammars. Formal definition The collection of regular languages over an alphabet Σ is defined recursively as follows: * The empty language Ø is a regular language. * For each ''a'' ∈ Σ (''a'' belongs to Σ), the singleton language is a regular language. * If ''A'' is a regular language, ''A''* ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamic Programming
Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. In both contexts it refers to simplifying a complicated problem by breaking it down into simpler sub-problems in a recursive manner. While some decision problems cannot be taken apart this way, decisions that span several points in time do often break apart recursively. Likewise, in computer science, if a problem can be solved optimally by breaking it into sub-problems and then recursively finding the optimal solutions to the sub-problems, then it is said to have ''optimal substructure''. If sub-problems can be nested recursively inside larger problems, so that dynamic programming methods are applicable, then there is a relation between the value of the larger problem and the values of the sub-problems.Cormen, T. H.; Leiserson, C. E.; Rives ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
