Miklós Ajtai

Miklós Ajtai (born 2 July 1946) is a computer scientist at the IBM Almaden Research Center, United States. In 2003, he received the Knuth Prize for his numerous contributions to the field, including a classic sorting network algorithm (developed jointly with J. Komlós and Endre Szemerédi), exponential lower bounds, superlinear time-space tradeoffs for branching programs, and other "unique and spectacular" results. He is a member of the U.S. National Academy of Sciences.^[2]

One of Ajtai's results states that the length of proofs in propositional logic of the pigeonhole principle for n items grows faster than any polynomial in n. He also proved that the statement "any two countable structures that are second-order equivalent are also isomorphic" is both consistent with and independent of ZFC. Ajtai and Szemerédi proved the corners theorem, an important step toward higher-dimensional generalizations of the Szemerédi theorem. With Komlós and Szemerédi, he proved the ct²/log t upper bound for the Ramsey number R(3,t). The corresponding lower bound was proved by Kim only in 1995, a result that earned him a Fulkerson Prize. With Chvátal, Newborn, and Szemerédi, Ajtai proved the crossing number inequality, that any drawing of a graph with n vertices and m edges, where m > 4n, has at least m³ / 100n² crossings. Ajtai and Dwork devised in 1997 a lattice-based public-key cryptosystem; Ajtai has done extensive work on lattice problems. For his numerous contributions in Theoretical Computer Science, he received the Knuth Prize.^[1]

Ajtai received his Candidate of Sciences degree in 1976 from the Hungarian Academy of Sciences.^[3] Since 1995, he has been an external member of the Hungarian Academy of Sciences.

In 1998, he was an Invited Speaker of the International Congress of Mathematicians in Berlin.^[4] In 2012, he was elected as a Fellow of the American Association for the Advancement of Science.^[5] In 2021, he was elected a member of the National Academy of Sciences.^[6]

• Ajtai, Miklós (10 May 2008). "Optimal lower bounds for the Korkine-Zolotareff parameters of a lattice and for Schnorr's algorithm for the shortest vector problem". Theory of Computing. 4: 21–51. doi:10.4086/toc.2008.v004a002.
• Ajtai, Miklós (5 October 2005). "A Non-linear Time Lower Bound for Boolean Branching Programs". Theory of Computing. 1: 149–176. doi:10.4086/toc.2005.v001a008.
• Ajtai, M. (1996). "Generating hard instances of lattice problems (Extended abstract)". Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC '96. pp. 99–108. doi:10.1145/237814.237838. ISBN 978-0-89791-785-8. S2CID 6864824.

1. Ajtai, M. (September 1979). "Isomorphism and higher order equivalence". Annals of Mathematical Logic. 16 (3): 181–203. doi:10.1016/0003-4843(79)90001-9.
2. Ajtai, M.; Komlós, J.; Szemerédi, E. (March 1982). "Largest random component of a k-cube". Combinatorica. 2 (1): 1–7. doi:10.1007/BF02579276. S2CID 7903662.

• Miklós Ajtai home page
• Miklós Ajtai publications indexed by Microsoft Academic
• Miklós Ajtai at the Mathematics Genealogy Project

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