|
Log-space Transducer
In computational complexity theory, a log space transducer (LST) is a type of Turing machine used for log-space reductions. A log space transducer, M, has three tapes: * A read-only ''input'' tape. * A read/write ''work'' tape (bounded to at most O(\log n) symbols). * A write-only, write-once ''output'' tape. M will be designed to compute a log-space computable function f\colon \Sigma^\ast \rightarrow \Sigma^\ast (where \Sigma is the alphabet of both the ''input'' and ''output'' tapes). If M is executed with w on its ''input'' tape, when the machine halts, it will have f(w) remaining on its ''output'' tape. A language A \subseteq \Sigma^\ast is said to be log-space reducible to a language B \subseteq \Sigma^\ast if there exists a log-space computable function f that will convert an input from problem A into an input to problem B in such a way that w \in A \iff f(w) \in B. This seems like a rather convoluted idea, but it has two useful properties that are desirable for a reducti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Complexity Theory
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of computationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turing Machine
A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algorithm. The machine operates on an infinite memory tape divided into discrete cells, each of which can hold a single symbol drawn from a finite set of symbols called the alphabet of the machine. It has a "head" that, at any point in the machine's operation, is positioned over one of these cells, and a "state" selected from a finite set of states. At each step of its operation, the head reads the symbol in its cell. Then, based on the symbol and the machine's own present state, the machine writes a symbol into the same cell, and moves the head one step to the left or the right, or halts the computation. The choice of which replacement symbol to write and which direction to move is based on a finite table that specifies what to do for each comb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Log-space Reduction
In computational complexity theory, a log-space reduction is a reduction computable by a deterministic Turing machine using logarithmic space. Conceptually, this means it can keep a constant number of pointers into the input, along with a logarithmic number of fixed-size integers.Arora & Barak (2009) p. 88 It is possible that such a machine may not have space to write down its own output, so the only requirement is that any given bit of the output be computable in log-space. Formally, this reduction is executed via a log-space transducer. Such a machine has polynomially-many configurations, so log-space reductions are also polynomial-time reductions. However, log-space reductions are probably weaker than polynomial-time reductions; while any non-empty, non-full language in P is polynomial-time reducible to any other non-empty, non-full language in P, a log-space reduction from an NL-complete language to a language in L, both of which would be languages in P, would imply the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Log-space Computable Function
In computational complexity theory, a log-space computable function is a function f\colon \Sigma^\ast \rightarrow \Sigma^\ast that requires only O(\log n) memory to be computed (this restriction does not apply to the size of the output). The computation is generally done by means of a log-space transducer. Log-space reductions The main use for log-space computable functions is in log-space reductions. This is a means of transforming an instance of one problem into an instance of another problem, using only logarithmic space. Examples of log-space computable functions * Function converting a problem of a non-deterministic Turing machine that decides a language ''A'' in log-space to ST-connectivity In computer science, st-connectivity or STCON is a decision problem asking, for vertices ''s'' and ''t'' in a directed graph, if ''t'' is reachable from ''s''. Formally, the decision problem is given by :. Complexity On a sequential computer ....Sipser (2006) International Se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alphabet (computer Science)
In formal language theory, an alphabet is a non-empty set of 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 (e.g., the alphabet of letters "a" through "z"), countable (e.g., \), or even uncountable (e.g., \). 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 , the binary alphabet, and a "00101111" is an example of a bin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
L (complexity)
In computational complexity theory, L (also known as LSPACE or DLOGSPACE) is the complexity class containing decision problems that can be solved by a deterministic Turing machine using a logarithmic amount of writable memory space., Definition 8.12, p. 295., p. 177. Formally, the Turing machine has two tapes, one of which encodes the input and can only be read, whereas the other tape has logarithmic size but can be read as well as written. Logarithmic space is sufficient to hold a constant number of pointers into the input and a logarithmic number of boolean flags, and many basic logspace algorithms use the memory in this way. Complete problems and logical characterization Every non-trivial problem in L is complete under log-space reductions, so weaker reductions are required to identify meaningful notions of L-completeness, the most common being first-order reductions. A 2004 result by Omer Reingold shows that USTCON, the problem of whether there exists a path ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer Press
Axel Springer SE () is a German digital and popular periodical publishing house which is the largest in Europe, with numerous multimedia news brands, such as '' Bild'', ''Die Welt'', and ''Fakt'' and more than 15,000 employees. It generated total revenues of about €3.3 billion and an EBITDA of €559 million in the financial year 2015. The digital media activities contribute more than 60% to its revenues and nearly 70% to its EBITDA. Axel Springer’s business is divided into three segments: paid models, marketing models, and classified ad models. Since 2020, it is majority-owned by the US private equity firm KKR. Headquartered in Berlin, Germany, the company is active in more than 40 countries, including subsidiaries, joint ventures, and licensing. It was started in 1946/1947 by journalist Axel Springer. Its current CEO is Mathias Döpfner. The Axel Springer company is the largest publishing house in Europe and controls the largest share of the German market for daily ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sipser, Michael
Michael Fredric Sipser (born September 17, 1954) is an American theoretical computer scientist who has made early contributions to computational complexity theory. He is a professor of applied mathematics and was the Dean of Science at the Massachusetts Institute of Technology. Biography Sipser was born and raised in Brooklyn, New York and moved to Oswego, New York when he was 12 years old. He earned his BA in mathematics from Cornell University in 1974 and his PhD in engineering from the University of California at Berkeley in 1980 under the direction of Manuel Blum.Trafton, Anne"Michael Sipser named dean of the School of Science: Sipser has served as interim dean since Marc Kastner’s departure" MIT News Office, June 5, 2014 He joined MIT's Laboratory for Computer Science as a research associate in 1979 and then was a Research Staff Member at IBM Research in San Jose. In 1980, he joined the MIT faculty. He spent the 1985-1986 academic year on the faculty of the Uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cengage Learning
Cengage Group is an American educational content, technology, and services company for the higher education, K-12, professional, and library markets. It operates in more than 20 countries around the world.(Jun 27, 2014Global Publishing Leaders 2014: Cengage publishersweekly.comCompany Info - Wall Street JournalCengage LearningCompany Overview of Cengage Learning, Inc. BloombergBusiness Company information The company is headquartered in Boston, Massachusetts, and has approximately 5,000 employees worldwide across nearly 38 countries. It was headquartered at its Stamford, Connecticut, office until April 2014. |
Computational Complexity Theory
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of computationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
