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Symmetric Turing Machine
A symmetric Turing machine is a Turing machine which has a configuration graph that is undirected (that is, configuration i yields configuration j if and only if j yields i). Definition of symmetric Turing machines Formally, we define a variant of Turing machines with a set of transitions of the form , where ''p,q'' are states, ''ab,cd'' are pairs of symbols and ''D'' is a direction. If ''D'' is ''left'', then the head of a machine in state ''p'' above a tape symbol ''b'' preceded by a symbol ''a'' can be transitioned by moving the head left, changing the state to ''q'' and replacing the symbols ''a,b'' by ''c,d''. The opposite transition can always be applied. If ''D'' is right the transition is analogous. The ability to peek at two symbols and change both at a time is non-essential, but makes the definition easier. Such machines were first defined in 1982 by Harry R. Lewis and Christos Papadimitriou, who were looking for a class in which to place USTCON, the problem aski ... [...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 com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The ACM
The ''Journal of the ACM'' is a peer-reviewed scientific journal covering computer science in general, especially theoretical aspects. It is an official journal of the Association for Computing Machinery. Its current editor-in-chief is Venkatesan Guruswami. The journal was established in 1954 and "computer scientists universally hold the ''Journal of the ACM'' in high esteem". See also * ''Communications of the ACM ''Communications of the ACM'' is the monthly journal of the Association for Computing Machinery (ACM). It was established in 1958, with Saul Rosen as its first managing editor. It is sent to all ACM members. Articles are intended for readers wi ...'' References External links * Publications established in 1954 Computer science journals Association for Computing Machinery academic journals Bimonthly journals English-language journals {{compu-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alan Turing
Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer. He is widely considered to be the father of theoretical computer science and artificial intelligence. Born in Maida Vale, London, Turing was raised in southern England. He graduated at King's College, Cambridge, with a degree in mathematics. Whilst he was a fellow at Cambridge, he published a proof demonstrating that some purely mathematical yes–no questions can never be answered by computation and defined a Turing machine, and went on to prove that the halting problem for Turing machines is undecidable. In 1938, he obtained his PhD from the Department of M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expander Graph
In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander constructions have spawned research in pure and applied mathematics, with several applications to complexity theory, design of robust computer networks, and the theory of error-correcting codes. Definitions Intuitively, an expander graph is a finite, undirected multigraph in which every subset of the vertices that is not "too large" has a "large" boundary. Different formalisations of these notions give rise to different notions of expanders: ''edge expanders'', ''vertex expanders'', and ''spectral expanders'', as defined below. A disconnected graph is not an expander, since the boundary of a connected component is empty. Every connected graph is an expander; however, different connected graphs have different expansion parameters. The complete graph has the best expansion property, but it has largest possible degree. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zig-zag Product
In graph theory, the zig-zag product of regular graphs G,H, denoted by G \circ H, is a binary operation which takes a large graph (G) and a small graph (H) and produces a graph that approximately inherits the size of the large one but the degree of the small one. An important property of the zig-zag product is that if H is a good expander, then the expansion of the resulting graph is only slightly worse than the expansion of G. Roughly speaking, the zig-zag product G \circ H replaces each vertex of G with a copy (cloud) of H, and connects the vertices by moving a small step (zig) inside a cloud, followed by a big step (zag) between two clouds, and finally performs another small step inside the destination cloud. The zigzag product was introduced by . When the zig-zag product was first introduced, it was used for the explicit construction of constant degree expanders and extractors. Later on, the zig-zag product was used in computational complexity theory to prove that symmetric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gödel Prize
The Gödel Prize is an annual prize for outstanding papers in the area of theoretical computer science, given jointly by the European Association for Theoretical Computer Science (EATCS) and the Association for Computing Machinery Special Interest Group on Algorithms and Computational Theory ( ACM SIGACT). The award is named in honor of Kurt Gödel. Gödel's connection to theoretical computer science is that he was the first to mention the "P versus NP" question, in a 1956 letter to John von Neumann in which Gödel asked whether a certain NP-complete problem could be solved in quadratic or linear time. The Gödel Prize has been awarded since 1993. The prize is awarded either at STOC (ACM Symposium on Theory of Computing, one of the main North American conferences in theoretical computer science) or ICALP ( International Colloquium on Automata, Languages and Programming, one of the main European conferences in the field). To be eligible for the prize, a paper must be published ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Salil Vadhan
Salil Vadhan is an American computer scientist. He is Vicky Joseph Professor of Computer Science and Applied Mathematics at Harvard University. After completing his undergraduate degree in Mathematics and Computer Science at Harvard in 1995, he obtained his PhD in Applied Mathematics from Massachusetts Institute of Technology in 1999, where his advisor was Shafi Goldwasser. His research centers around the interface between computational complexity theory and cryptography. He focuses on the topics of pseudorandomness and zero-knowledge proofs. His work on the zig-zag product, with Omer Reingold and Avi Wigderson, was awarded the 2009 Gödel Prize. Contributions Zig-zag graph product for constructing expander graphs One of the main contributions of his work is a new type of graph product, called the zig-zag product. Taking a product of a large graph with a small graph, the resulting graph inherits (roughly) its size from the large one, its degree from the small one, and its ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Avi Wigderson
Avi Wigderson ( he, אבי ויגדרזון; born 9 September 1956) is an Israeli mathematician and computer scientist. He is the Herbert H. Maass Professor in the school of mathematics at the Institute for Advanced Study in Princeton, New Jersey, United States of America. His research interests include complexity theory, parallel algorithms, graph theory, cryptography, distributed computing, and neural networks. Wigderson received the Abel Prize in 2021 for his work in theoretical computer science. Biography Avi Wigderson was born in Haifa, Israel, to Holocaust survivors. Wigderson is a graduate of the Hebrew Reali School in Haifa, and did his undergraduate studies at the Technion in Haifa, Israel, graduating in 1980, and went on to graduate study at Princeton University. He received his PhD in computer science in 1983 after completing a doctoral dissertation, titled "Studies in computational complexity", under the supervision of Richard Lipton. After short-term positions at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grace Murray Hopper Award
The Grace Murray Hopper Award (named for computer pioneer RADM Grace Hopper) has been awarded by the Association for Computing Machinery (ACM) since 1971. The award goes to a computer professional who makes a single, significant technical or service contribution at or before age 35. __TOC__ Recipients * 1971 Donald Knuth * 1972 Paul H. Dirksen * 1972 Paul H. Cress * 1973 Lawrence M. Breed * 1973 Richard H. Lathwell * 1973 Roger Moore * 1974 George N. Baird * 1975 Allan L. Scherr * 1976 Edward H. Shortliffe * 1977 ''no award'' * 1978 Ray Kurzweil * 1979 Steve Wozniak * 1980 Robert M. Metcalfe * 1981 Daniel S. Bricklin * 1982 Brian K. Reid * 1983 ''no award'' * 1984 Daniel Henry Holmes Ingalls, Jr. * 1985 Cordell Green * 1986 William Nelson "Bill" Joy * 1987 John Ousterhout * 1988 Guy L. Steele Jr. * 1989 W. Daniel Hillis * 1990 Richard Stallman * 1991 Feng-hsiung Hsu * 1992 ''no award'' * 1993 Bjarne Stroustrup * 1994–1995 ''no award'' * 1996 Shafrira Goldwass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Omer Reingold
Omer Reingold ( he, עומר ריינגולד) is an Israeli computer scientist. He is the Rajeev Motwani professor of Computer Science in the Computer Science Department at Stanford University and the director of thSimons Collaboration on the Theory of Algorithmic Fairness He received a PhD in computer science at Weizmann in 1998 under Moni Naor. He received the 2005 Grace Murray Hopper Award for his work in finding a deterministic logarithmic-space algorithm for st-connectivity in undirected graphs. He, along with Avi Wigderson and Salil Vadhan, won the Gödel Prize (2009) for their work on the zig-zag product. He became a Fellow of the Association for Computing Machinery in 2014 ''"For contributions to the study of pseudorandomness, derandomization, and cryptography Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or '' -logia'', "study", respectively), is the practice and study of techniques for secu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Configuration Graph
Configuration graphs are a theoretical tool used in computational complexity theory to prove a relation between graph reachability and complexity classes. Definition A theoretical computational model, like Turing machine or finite automata, explains how to do a computation. The model explains both what is an initial configuration of the machine and which steps can be taken to continue the computation, until we eventually stop. A ''configuration'', also called an ''Instantaneous Description (ID)'' is a finite representation of the machine at a given time. For example, for a finite automata and a given input, the configuration will be the current state and the number of read letters, for a Turing machine it will be the state, the content of the tape and the position of the head. A configuration graph is a directed labeled graph where the label of the vertices are the possible configurations of the models and where there is an edge from one configuration to another if it correspond t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logspace
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 b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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