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PCP Theorem
In computational complexity theory, the PCP theorem (also known as the PCP characterization theorem) states that every decision problem in the NP complexity class has probabilistically checkable proofs ( proofs that can be checked by a randomized algorithm) of constant query complexity and logarithmic randomness complexity (uses a logarithmic number of random bits). The PCP theorem says that for some universal constant K, for every n, any mathematical proof for a statement of length n can be rewritten as a different proof of length \operatorname(n) that is formally verifiable with 99% accuracy by a randomized algorithm that inspects only K letters of that proof. The PCP theorem is the cornerstone of the theory of computational hardness of approximation, which investigates the inherent difficulty in designing efficient approximation algorithms for various optimization problems. It has been described by Ingo Wegener as "the most important result in complexity theory since C ... [...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 explores the relationships between these classifications. 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 logic gate, gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Satisfiability Problem
In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) asks whether there exists an Interpretation (logic), interpretation that Satisfiability, satisfies a given Boolean logic, Boolean Formula (mathematical logic), formula. In other words, it asks whether the formula's variables can be consistently replaced by the values TRUE or FALSE to make the formula evaluate to TRUE. If this is the case, the formula is called ''satisfiable'', else ''unsatisfiable''. For example, the formula "''a'' AND NOT ''b''" is satisfiable because one can find the values ''a'' = TRUE and ''b'' = FALSE, which make (''a'' AND NOT ''b'') = TRUE. In contrast, "''a'' AND NOT ''a''" is unsatisfiable. SAT is the first problem that was proven to be NP-complete—this is the Cook–Levin theorem. This means that all problems in the complexity class NP (complexity), NP, which includes a wide range of natu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
László Lovász
László Lovász (; born March 9, 1948) is a Hungarian mathematician and professor emeritus at Eötvös Loránd University, best known for his work in combinatorics, for which he was awarded the 2021 Abel Prize jointly with Avi Wigderson. He was the president of the International Mathematical Union from 2007 to 2010 and the president of the Hungarian Academy of Sciences from 2014 to 2020. In graph theory, Lovász's notable contributions include the proofs of Kneser's conjecture and the Lovász local lemma, as well as the formulation of the Erdős–Faber–Lovász conjecture. He is also one of the eponymous authors of the LLL lattice reduction algorithm. Early life and education Lovász was born on March 9, 1948, in Budapest, Hungary. Lovász attended the Fazekas Mihály Gimnázium in Budapest. He won three gold medals (1964–1966) and one silver medal (1963) at the International Mathematical Olympiad. He also participated in a Hungarian game show about math prodigi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carsten Lund
Carsten Lund (born July 1, 1963) is a Danish-born theoretical computer scientist, currently working at AT&T Labs in Bedminster, New Jersey, United States. Lund was born in Aarhus, Denmark, and received the "kandidat" degree in 1988 from the University of Aarhus and his Ph.D. from the University of Chicago in computer science. His thesis, entitled The Power of Interaction, was chosen as an ACM 'Distinguished Dissertation'. Lund was a co-author on two of five competing papers at the 1990 Symposium on Foundations of Computer Science characterizing complexity classes such as PSPACE and NEXPTIME in terms of interactive proof systems; this work became part of his 1991 Ph.D. thesis from the University of Chicago under the supervision of Lance Fortnow and László Babai, for which he was a runner-up for the 1991 ACM Doctoral Dissertation Award. He is also known for his joint work with Sanjeev Arora, Madhu Sudan, Rajeev Motwani, and Mario Szegedy that discovered the existence of probab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shafi Goldwasser
Shafrira Goldwasser (; born 1959) is an Israeli-American computer scientist. A winner of the Turing Award in 2012, she is the RSA Professor of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology; a professor of mathematical sciences at the Weizmann Institute of Science; the former director of the Simons Institute for the Theory of Computing at the University of California, Berkeley; and co-founder and chief scientist of Duality Technologies. Education and early life Born in New York City, Goldwasser obtained her bachelor's degree in 1979 in mathematics and science from Carnegie Mellon University, Carnegie Mellon. She continued her studies in computer science at University of California, Berkeley, Berkeley, receiving a master's degree in 1981 and a PhD in 1984. While at Berkeley, she and her doctoral advisor, Manuel Blum, would propose the Blum-Goldwasser cryptosystem. Career and research Goldwasser joined Massachusetts Institute of Technology ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uriel Feige
Uriel Feige () is an Israeli computer scientist who was a doctoral student of Adi Shamir. Life Uriel Feige currently holds the post of Professor at the Department of Computer Science and Applied Mathematics, the Weizmann Institute of Science, Rehovot in Israel. Work He is notable for co-inventing the Feige–Fiat–Shamir identification scheme along with Amos Fiat and Adi Shamir. Honors and awards He won the Gödel Prize in 2001 "for the PCP theorem and its applications to hardness of approximation In computer science, hardness of approximation is a field that studies the algorithmic complexity of finding near-optimal solutions to optimization problems. Scope Hardness of approximation complements the study of approximation algorithms by pro ...". References {{DEFAULTSORT:Feige, Uriel Living people Gödel Prize laureates Israeli theoretical computer scientists Public-key cryptographers 20th-century Israeli mathematicians 21st-century Israeli mathematicians Israe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sanjeev Arora
Sanjeev Arora (born January 1968) is an Indian-American theoretical computer scientist who works in AI and Machine learning. Life Sanjeev scored the IIT JEE number 1 rank in 1986 He was a visiting scholar at the Institute for Advanced Study in 2002–03. In 2008 he was inducted as a Fellow of the Association for Computing Machinery. In 2011 he was awarded thACM Infosys Foundation Award(now renamed ACM Prize in Computing), given to mid-career researchers in Computer Science. He is a two-time recipient of the Gödel Prize (2001 & 2010). Arora has been awarded the Fulkerson Prize for 2012 for his work on improving the approximation ratio for graph separators and related problems from O(\log n) to O(\sqrt) (jointly with Satish Rao and Umesh Vazirani). In 2012 he became a Simons Investigator. Arora was elected in 2015 to the American Academy of Arts and Sciences and in 2018 to the National Academy of Sciences. He was a plenary speaker at the 2018 International Congress of Math ... [...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 alternately at ICALP (even years) and STOC (odd years). STOC is the ACM Symposium on Theory of Computing, one of the main North American conferences in theoretical computer science, whereas ICALP is the International Colloquium on Automata, Languages and Programming, one of the main Europe Europe is a c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lance Fortnow
Lance Jeremy Fortnow (born August 15, 1963) is a computer scientist known for major results in Computational complexity theory, computational complexity and interactive proof systems. Since 2019, he has been at the Illinois Institute of Technology, where he is currently the Dean of the College of Computing. Biography Lance Fortnow received a doctorate in applied mathematics from MIT in 1989, supervised by Michael Sipser. Since graduation, he has been on the faculty of the University of Chicago (1989–1999, 2003–2007), Northwestern University (2008–2012) and the Georgia Institute of Technology (2012–2019) as chair of the Georgia Institute of Technology School of Computer Science, School of Computer Science. From 1999-2003 he was a Senior Research Scientist at the NEC Research Institute. Fortnow was the founding editor-in-chief of the journal ''ACM Transactions on Computation Theory'' in 2009. He was the chair of ACM SIGACT and succeeded by Paul Beame. He was the chair of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probabilistically Checkable Proof
In computational complexity theory, a probabilistically checkable proof (PCP) is a type of proof that can be checked by a randomized algorithm using a bounded amount of randomness and reading a bounded number of bits of the proof. The algorithm is then required to accept correct proofs and reject incorrect proofs with very high probability. A standard proof (or certificate), as used in the verifier-based definition of the complexity class NP, also satisfies these requirements, since the checking procedure deterministically reads the whole proof, always accepts correct proofs and rejects incorrect proofs. However, what makes them interesting is the existence of probabilistically checkable proofs that can be checked by reading only a few bits of the proof using randomness in an essential way. Probabilistically checkable proofs give rise to many complexity classes depending on the number of queries required and the amount of randomness used. The class refers to the set of decision ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interactive Proof System
In computational complexity theory, an interactive proof system is an abstract machine that models computation as the exchange of messages between two parties: a ''prover'' and a ''verifier''. The parties interact by exchanging messages in order to ascertain whether a given string belongs to a language or not. The prover is assumed to possess unlimited computational resources but cannot be trusted, while the verifier has bounded computation power but is assumed to be always honest. Messages are sent between the verifier and prover until the verifier has an answer to the problem and has "convinced" itself that it is correct. All interactive proof systems have two requirements: * Completeness: if the statement is true, the honest prover (that is, one following the protocol properly) can convince the honest verifier that it is indeed true. * Soundness: if the statement is false, no prover, even if it doesn't follow the protocol, can convince the honest verifier that it is true, excep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SIGACT News
ACM SIGACT or SIGACT is the Association for Computing Machinery Special Interest Group on Algorithms and Computation Theory, whose purpose is support of research in theoretical computer science. It was founded in 1968 by Patrick C. Fischer. Publications SIGACT publishes a quarterly print newsletter, ''SIGACT News''. Its online version, ''SIGACT News Online'', is available since 1996 for SIGACT members, with unrestricted access to some features. Conferences SIGACT sponsors or has sponsored several annual conferences. *COLT: Conference on Learning Theory, until 1999 *PODC: ACM Symposium on Principles of Distributed Computing (jointly sponsored by SIGOPS) *PODS: ACM Symposium on Principles of Database Systems (jointly sponsored by SIGAI and SIGACT) *POPL: ACM Symposium on Principles of Programming Languages *SOCG: ACM Symposium on Computational Geometry (jointly sponsored by SIGGRAPH), until 2014 *SODA: ACM/SIAM Symposium on Discrete Algorithms (jointly sponsored by the Society ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
