This article relies largely or entirely on a single source. (December 2009)
2 July 1946|
Budapest, Second Republic of Hungary
|Residence||San Jose, California, United States|
|Alma mater||Hungarian Academy of Sciences|
|Awards||Knuth Prize (2003)|
|Fields||Computational complexity theory|
|Institutions||IBM Almaden Research Center|
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.
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.
- Ajtai, M. (1979), "Isomorphism and higher order equivalence", Annals of Mathematical Logic, 16 (3): 181–203, doi:10.1016/0003-4843(79)90001-9.
- Ajtai, M.; Komlós, J.; Szemerédi, E. (1982), "Largest random component of a k-cube", Combinatorica, 2 (1): 1–7, doi:10.1007/BF02579276.
- Magyar Tudományos Akadémia, Almanach, 1986, Budapest.
- Miklós Ajtai home page
- List of publications from Microsoft Academic
- Miklós Ajtai at the Mathematics Genealogy Project
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