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Manuel Blum
Manuel Blum (born 26 April 1938) is a Venezuelan-born American computer scientist who received the Turing Award in 1995 "In recognition of his contributions to the foundations of computational complexity theory and its application to cryptography and program checking". Education Blum was born to a Jewish family in Venezuela. Blum was educated at MIT, where he received his bachelor's degree and his master's degree in electrical engineering in 1959 and 1961 respectively. In MIT, he was recommended to Warren S. McCulloch, and they collaborated on some mathematical problems in neural networks. He obtained a Ph.D. in mathematics in 1964 supervised by Marvin Minsky.. Career Blum worked as a professor of computer science at the University of California, Berkeley until 2001. From 2001 to 2018, he was the Bruce Nelson Professor of Computer Science at Carnegie Mellon University, where his wife, Lenore Blum, was also a professor of computer science. In 2002, he was elected to the Unit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lenore Blum
Lenore Carol Blum (née Epstein, born December 18, 1942) is an American computer scientist and mathematician who has made contributions to the theories of real number computation, cryptography, and pseudorandom number generation. She was a distinguished career professor of computer science at Carnegie Mellon University until 2019 and is currently a professor in residence at the University of California, Berkeley. She is also known for her efforts to increase diversity in mathematics and computer science. Early life and education Blum was born to a Jewish family in New York City, where her mother was a science teacher. They moved to Venezuela when Blum was nine. After graduating from her Venezuelan high school at age 16, she studied architecture at Carnegie Institute of Technology (now Carnegie Mellon University) beginning in 1959. With the assistance of Alan Perlis, she shifted fields to mathematics in 1960. She married Manuel Blum, then a student at the Massachusetts Institute ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Silvio Micali
Silvio Micali (born October 13, 1954) is an Italian computer scientist, professor at the Massachusetts Institute of Technology and the founder of Algorand, a proof-of-stake blockchain cryptocurrency protocol. Micali's research at the MIT Computer Science and Artificial Intelligence Laboratory centers on cryptography and information security. In 2012, he received the Turing Award for his work in cryptography. Personal life Micali graduated in mathematics at La Sapienza University of Rome in 1978 and earned a PhD degree in computer science from the University of California, Berkeley in 1982; for research supervised by Manuel Blum. Micali has been on the faculty of MIT's Electrical Engineering and Computer Science Department since 1983. He has also served on the faculty of the University of Pennsylvania, University of Toronto, and Tsinghua University. His research interests are cryptography, zero knowledge, pseudorandom generation, secure protocols, and mechanism design. Car ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blum's Speedup Theorem
In computational complexity theory, Blum's speedup theorem, first stated by Manuel Blum in 1967, is a fundamental theorem about the complexity of computable functions. Each computable function has an infinite number of different program representations in a given programming language. In the theory of algorithms one often strives to find a program with the smallest complexity for a given computable function and a given complexity measure (such a program could be called ''optimal''). Blum's speedup theorem shows that for any complexity measure, there exists a computable function such that there is no optimal program computing it, because every program has a program of lower complexity. This also rules out the idea that there is a way to assign to arbitrary functions ''their'' computational complexity, meaning the assignment to any ''f'' of the complexity of an optimal program for ''f''. This does of course not exclude the possibility of finding the complexity of an optimal program f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blum Integer
In mathematics, a natural number ''n'' is a Blum integer if is a semiprime for which ''p'' and ''q'' are distinct prime numbers congruent to 3 mod 4.Joe Hurd, Blum Integers (1997), retrieved 17 Jan, 2011 from http://www.gilith.com/research/talks/cambridge1997.pdf That is, ''p'' and ''q'' must be of the form , for some integer ''t''. Integers of this form are referred to as Blum primes. Goldwasser, S. and Bellare, M.br>"Lecture Notes on Cryptography". Summer course on cryptography, MIT, 1996-2001 This means that the factors of a Blum integer are Gaussian primes with no imaginary part. The first few Blum integers are : 21, 33, 57, 69, 77, 93, 129, 133, 141, 161, 177, 201, 209, 213, 217, 237, 249, 253, 301, 309, 321, 329, 341, 381, 393, 413, 417, 437, 453, 469, 473, 489, 497, ... The integers were named for computer scientist Manuel Blum. Properties Given a Blum integer, ''Q''''n'' the set of all quadratic residues modulo ''n'' and coprime to ''n'' and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blum Complexity Axioms
In computational complexity theory the Blum axioms or Blum complexity axioms are axioms that specify desirable properties of complexity measures on the set of computable functions. The axioms were first defined by Manuel Blum in 1967. Importantly, Blum's speedup theorem and the Gap theorem hold for any complexity measure satisfying these axioms. The most well-known measures satisfying these axioms are those of time (i.e., running time) and space (i.e., memory usage). Definitions A Blum complexity measure is a pair (\varphi, \Phi) with \varphi a numbering of the partial computable functions \mathbf^ and a computable function :\Phi: \mathbb \to \mathbf^ which satisfies the following Blum axioms. We write \varphi_i for the ''i''-th partial computable function under the Gödel numbering \varphi, and \Phi_i for the partial computable function \Phi(i). * the domains of \varphi_i and \Phi_i are identical. * the set \ is recursive. Examples * (\varphi, \Phi) is a complexity m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ryan Williams (computer Scientist)
Ryan Williams may refer to: Sports *Ryan Williams (running back) (born 1990), American football player *Ryan Williams (wide receiver) (born 2007), American football player *Ryan Williams (Australian rules footballer) (born 1988), Australian former Australian rules footballer *Ryan Williams (BMX rider) (born 1994), Australian freestyle BMX and scooter rider *Ryan Williams (footballer, born 1978), English footballer *Ryan Williams (footballer, born 1991), English footballer *Ryan Williams (men's soccer, born 1996), American soccer midfielder *Ryan Williams (soccer, born 1993), Australian soccer winger, playing for Perth Glory *Ryan Williams (women's soccer) (born 1996), American soccer defender Other *Ryan Williams (computer scientist) (born 1979), American computer scientist *Ryan Williams (entrepreneur) (born 1988), technology entrepreneur *Ryan Williams (American politician) (born 1973), member of the Tennessee House of Representatives *Ryan Williams (Canadian politician) *Ryan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luis Von Ahn
Luis von Ahn (; born 19 August 1978) is a Guatemalan-American entrepreneur and software developer. He is the founder of the company reCAPTCHA, which was sold to Google in 2009, and the co-founder and CEO of Duolingo. For these projects and others, von Ahn is known as one of the pioneers of crowdsourcing. von Ahn was a professor in the Computer Science Department at Carnegie Mellon University. Early life and education Luis von Ahn was born and raised in Guatemala City. He is of German descent. His mother was one of the first women in Guatemala to complete medical school. She gave birth to von Ahn at age 42, and raised him as a single mother. He attended the American School of Guatemala, a private English-language school in Guatemala City, an experience he cites as a great privilege. When von Ahn was eight years old, his mother bought him a Commodore 64 computer, beginning his fascination with technology and computer science. When he applied to colleges in the United State ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vijay Vazirani
Vijay Virkumar Vazirani (; b. 1957) is an Indian American distinguished professor of computer science in the Donald Bren School of Information and Computer Sciences at the University of California, Irvine. Education and career Vazirani first majored in electrical engineering at Indian Institute of Technology, Delhi but in his second year he transferred to MIT and received his bachelor's degree in computer science from MIT in 1979 and his Ph.D. from the University of California, Berkeley in 1983. His dissertation, ''Maximum Matchings without Blossoms'', was supervised by Manuel Blum. After postdoctoral research with Michael O. Rabin and Leslie Valiant at Harvard University, he joined the faculty at Cornell University in 1984. He moved to the IIT Delhi as a full professor in 1990, and moved again to the Georgia Institute of Technology in 1995. He was also a McKay Visiting Professor at the University of California, Berkeley, and a Distinguished SISL Visitor at the Social and Info ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Umesh Vazirani
Umesh Virkumar Vazirani is an Indian–American academic who is the Roger A. Strauch Professor of Electrical Engineering and Computer Science at the University of California, Berkeley, and the director of the Berkeley Quantum Computation Center. His research interests lie primarily in quantum computing. He is also a co-author of a textbook on algorithms.Algorithms: Dasgupta, Papadimitriou, Vazirani Biography Vazirani received a BS from MIT in 1981 and received his Ph.D. in 1986 from UC Berkeley under the supervision of Manuel Blum. He is the brother of University of California, Irvine professor Vijay Vazirani. Research Vazirani is one of the founders of the field of quantum computing. His 1993 paper with his student Ethan Bernstein on quantum complexity theory defined a model of quantum Turing machines which was amenable to complexity based analysis. This paper also gave an algorithm for the quantum Fourier transform, which was then used by Peter Shor within a year in his celeb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Sipser
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. 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 University of California at Berkeley and then returned to MIT. From 2004 until 2014, he served as head of the MIT Mathematics department. He was appointed Interim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jeffrey Shallit
Jeffrey Outlaw Shallit (born October 17, 1957) is an American computer scientist and mathematician. He is an active number theorist and a noted critic of intelligent design. He is married to Anna Lubiw, also a computer scientist. Early life and education Shallit was born in Philadelphia, Pennsylvania, in 1957. His father was journalist Joseph Shallit, the son of Jewish immigrants from Vitebsk, Russia (now in Belarus). His mother was Louise Lee Outlaw Shallit, a writer. He has one brother, Jonathan Shallit, a music professor. Shallit earned a Bachelor of Arts (B.A.) in mathematics from Princeton University in June 1979. He received a Ph.D., also in mathematics, from the University of California, Berkeley, in June 1983. His doctoral thesis was entitled ''Metric Theory of Pierce Expansions'' and his advisor was Manuel Blum. Advocacy Since 1996, Shallit has held the position of Vice-President of Electronic Frontier Canada. In 1997, he gained attention for the public ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steven Rudich
Steven Rudich (; October 4, 1961 – October 29, 2024) was an American computational theorist. He was a professor in the Carnegie Mellon School of Computer Science. In 1994, he and Alexander Razborov proved that a large class of combinatorial arguments, dubbed natural proofs, was unlikely to answer many of the important problems in computational complexity theory. For this work, they were awarded the Gödel Prize in 2007. He also co-authored a paper demonstrating that all currently known NP-complete problems remain NP-complete even under AC0 or NC0 reductions. Amongst Carnegie Mellon students, he is best known as the teacher of the class "Great Theoretical Ideas in Computer Science" (formerly named "How to Think Like a Computer Scientist"), often considered one of the most difficult classes in the undergraduate computer science curriculum. He was a long-time editor of the ''Journal of Cryptology'', as well as an accomplished magician. His Erdős number is 2. Leap@CMU Rudich ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |