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Miklós Ajtai (born 2 July 1946) is a computer scientist at the IBM Almaden Research Center, USA. 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 that any drawing of a graph with n vertices and m edges, where m > 4n, has at least m3 / 100n2 crossings.
Ajtai received his Candidate of Sciences degree in 1976 from the Hungarian Academy of Sciences. Since 1995 he has been an external member of the Hungarian Academy of Sciences.
- 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.