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Sardinas–Patterson Algorithm
In coding theory, the Sardinas–Patterson algorithm is a classical algorithm for determining in polynomial time whether a given variable-length code is uniquely decodable, named after August Albert Sardinas and George W. Patterson, who published it in 1953. The algorithm carries out a systematic search for a string which admits two different decompositions into codewords. As Knuth reports, the algorithm was rediscovered about ten years later in 1963 by Floyd, despite the fact that it was at the time already well known in coding theory. Idea of the algorithm Consider the code \. This code, which is based on an example by Berstel, is an example of a code which is not uniquely decodable, since the string :011101110011 can be interpreted as the sequence of codewords :01110 – 1110 – 011, but also as the sequence of codewords :011 – 1 – 011 – 10011. Two possible decodings of this encoded string are thus given by ''cdb'' and ''babe''. In general, a codeword can be foun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coding Theory
Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and computer data storage, data storage. Codes are studied by various scientific disciplines—such as information theory, electrical engineering, mathematics, linguistics, and computer science—for the purpose of designing efficient and reliable data transmission methods. This typically involves the removal of redundancy and the correction or detection of errors in the transmitted data. There are four types of coding: # Data compression (or ''source coding'') # Error detection and correction, Error control (or ''channel coding'') # Cryptography, Cryptographic coding # Line code, Line coding Data compression attempts to remove unwanted redundancy from the data from a source in order to transmit it more efficiently. For example, DEFLATE data compression makes files small ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NL-complete
In computational complexity theory, NL-complete is a complexity class containing the languages that are complete for NL, the class of decision problems that can be solved by a nondeterministic Turing machine using a logarithmic amount of memory space. The NL-complete languages are the most "difficult" or "expressive" problems in NL. If a deterministic algorithm exists for solving any one of the NL-complete problems in logarithmic memory space, then NL = L. Definitions NL consists of the decision problems that can be solved by a nondeterministic Turing machine with a read-only input tape and a separate read-write tape whose size is limited to be proportional to the logarithm of the input length. Similarly, L consists of the languages that can be solved by a deterministic Turing machine with the same assumptions about tape length. Because there are only a polynomial number of distinct configurations of these machines, both L and NL are subsets of the class P of determin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithms
In mathematics and computer science, an algorithm () 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 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 without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an effective method, an algorithm can be expressed within a finite amount of space and time"Any classic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert G
The name Robert is an ancient Germanic given name, from Proto-Germanic "fame" and "bright" (''Hrōþiberhtaz''). Compare Old Dutch ''Robrecht'' and Old High German ''Hrodebert'' (a compound of ''Hrōþ, Hruod'' () "fame, glory, honour, praise, renown, godlike" and ''berht'' "bright, light, shining"). It is the second most frequently used given name of ancient Germanic origin.Reaney & Wilson, 1997. ''Dictionary of English Surnames''. Oxford University Press. It is also in use Robert (surname), as a surname. Another commonly used form of the name is Rupert (name), Rupert. After becoming widely used in Continental Europe, the name entered England in its Old French form ''Robert'', where an Old English cognate form (''Hrēodbēorht'', ''Hrodberht'', ''Hrēodbēorð'', ''Hrœdbœrð'', ''Hrœdberð'', ''Hrōðberχtŕ'') had existed before the Norman Conquest. The feminine version is Roberta (given name), Roberta. The Italian, Portuguese, and Spanish form is Roberto (given name), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institute Of Radio Engineers
The Institute of Radio Engineers (IRE) was a professional organization which existed from 1912 until December 31, 1962. On January 1, 1963, it merged with the American Institute of Electrical Engineers (AIEE) to form the Institute of Electrical and Electronics Engineers (IEEE). Founding Following several attempts to form a technical organization of wireless practitioners in 1908–1912, the Institute of Radio Engineers (IRE) was finally established in 1912 in New York City. Among its founding organizations were the Society of Wireless Telegraph Engineers (SWTE) and the Wireless Institute (TWI). At the time, the dominant organization of electrical engineers was the American Institute of Electrical Engineers (AIEE). Many of the founding members of IRE considered AIEE too conservative and too focused on electric power. Moreover, the founders of the IRE sought to establish an international organization (unlike the “American” AIEE), and adopted a tradition of electing some ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessment to form Cambridge University Press and Assessment under Queen Elizabeth II's approval in August 2021. With a global sales presence, publishing hubs, and offices in more than 40 countries, it published over 50,000 titles by authors from over 100 countries. Its publications include more than 420 academic journals, monographs, reference works, school and university textbooks, and English language teaching and learning publications. It also published Bibles, runs a bookshop in Cambridge, sells through Amazon, and has a conference venues business in Cambridge at the Pitt Building and the Sir Geoffrey Cass Sports and Social Centre. It also served as the King's Printer. Cambridge University Press, as part of the University of Cambridge, was a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Post's Correspondence Problem
The Post correspondence problem is an undecidable decision problem that was introduced by Emil Post in 1946. Because it is simpler than the halting problem and the ''Entscheidungsproblem'' it is often used in proofs of undecidability. Definition of the problem Let A be an alphabet with at least two symbols. The input of the problem consists of two finite lists \alpha_, \ldots, \alpha_ and \beta_, \ldots, \beta_ of words over A. A solution to this problem is a sequence of indices (i_k)_ with K \ge 1 and 1 \le i_k \le N for all k, such that : \alpha_ \ldots \alpha_ = \beta_ \ldots \beta_. The decision problem then is to decide whether such a solution exists or not. Alternative definition :g: (i_1,\ldots,i_K) \mapsto \alpha_ \ldots \alpha_ :h: (i_1,\ldots,i_K) \mapsto \beta_ \ldots \beta_. This gives rise to an equivalent alternative definition often found in the literature, according to which any two homomorphisms g,h with a common domain and a common codomain form an i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Timeline Of Information Theory
A timeline of events related to information theory, quantum information theory and statistical physics, data compression, error correcting codes and related subjects. * 1872 – Ludwig Boltzmann presents his H-theorem, and with it the formula Σ''p''i log ''p''i for the entropy of a single gas particle * 1878 – J. Willard Gibbs defines the Gibbs entropy: the probabilities in the entropy formula are now taken as probabilities of the state of the ''whole'' system * 1924 – Harry Nyquist discusses quantifying and the speed at which it can be transmitted by a communication system * 1927 – John von Neumann defines the von Neumann entropy, extending the Gibbs entropy to quantum mechanics * 1928 – Ralph Hartley introduces Hartley information as the logarithm of the number of possible messages, with information being communicated when the receiver can distinguish one sequence of symbols from any other (regardless of any associated meaning) * 1929 – ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Block Code
In coding theory, block codes are a large and important family of Channel coding, error-correcting codes that encode data in blocks. There is a vast number of examples for block codes, many of which have a wide range of practical applications. The abstract definition of block codes is conceptually useful because it allows coding theorists, mathematicians, and computer scientists to study the limitations of ''all'' block codes in a unified way. Such limitations often take the form of ''bounds'' that relate different parameters of the block code to each other, such as its rate and its ability to detect and correct errors. Examples of block codes are Reed–Solomon codes, Hamming codes, Hadamard codes, Expander codes, Golay code (other), Golay codes, Reed–Muller codes and Polar code (coding theory), Polar codes. These examples also belong to the class of linear codes, and hence they are called linear block codes. More particularly, these codes are known as algebraic block ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prefix Code
A prefix code is a type of code system distinguished by its possession of the prefix property, which requires that there is no whole Code word (communication), code word in the system that is a prefix (computer science), prefix (initial segment) of any other code word in the system. It is trivially true for fixed-length codes, so only a point of consideration for variable-length code, variable-length codes. For example, a code with code has the prefix property; a code consisting of does not, because "5" is a prefix of "59" and also of "55". A prefix code is a uniquely decodable code: given a complete and accurate sequence, a receiver can identify each word without requiring a special marker between words. However, there are uniquely decodable codes that are not prefix codes; for instance, the reverse of a prefix code is still uniquely decodable (it is a suffix code), but it is not necessarily a prefix code. Prefix codes are also known as prefix-free codes, prefix condition codes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arto Salomaa
Arto Kustaa Salomaa (6 June 1934 – 26 January 2025) was a Finnish mathematician and computer scientist. His research career, which spanned over 40 years, was focused on formal languages and automata theory. Early life and education Salomaa was born in Turku, Finland on 6 June 1934. He earned a Bachelor's degree from the University of Turku in 1954 and a PhD from the same university in 1960. Salomaa's father was a professor of philosophy at the University of Turku. Salomaa was introduced to the theory of automata and formal languages during seminars at Berkeley given by John Myhill in 1957. Career In 1965 Salomaa became a professor of mathematics at the University of Turku, a position he retired from in 1999. He also spent two years in the late 1960s at the University of Western Ontario in London, Ontario, Canada, and two years in the 1970s at Aarhus University in Aarhus, Denmark.. Salomaa was president of the European Association for Theoretical Computer Science ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
