Alexander Razborov

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Alexander Razborov
Born (1963-02-16) February 16, 1963 (age 55)
NationalityUnited States, Russia
Alma materMoscow State University
Known forgroup theory, logic in computer science, theoretical computer science
AwardsNevanlinna Prize (1990)
Gödel Prize (2007)
David P. Robbins Prize (2013)
Scientific career
InstitutionsUniversity of Chicago, Steklov Mathematical Institute, Toyota Technological Institute at Chicago
Doctoral advisorSergei Adian

Aleksandr Aleksandrovich Razborov (Russian: Алекса́ндр Алекса́ндрович Разбо́ров; born February 16, 1963), sometimes known as Sasha Razborov, is a Soviet and Russian mathematician and computational theorist. He is Andrew McLeish Distinguished Service Professor at the University of Chicago.


In his best known work, joint with Steven Rudich, he introduced the notion of natural proofs, a class of strategies used to prove fundamental lower bounds in computational complexity. In particular, Razborov and Rudich showed that, under the assumption that certain kinds of one-way functions exist, such proofs cannot give a resolution of the P = NP problem, so new techniques will be required in order to solve this question.



  • Razborov, A. A. (1985). "Lower bounds for the monotone complexity of some Boolean functions" (PDF). Soviet Mathematics - Doklady. 31: 354–357.
  • Razborov, A. A. (June 1985). "Lower bounds on monotone complexity of the logical permanent". Mathematical Notes of the Academy of Sciences of the USSR. 37 (6): 485–493. doi:10.1007/BF01157687.
  • Разборов, Александр Александрович (1987). О системах уравнений в свободной группе (PDF) (in Russian). Московский государственный университет. (PhD thesis. 32.56MB)
  • Razborov, A. A. (April 1987). "Lower bounds on the size of bounded depth circuits over a complete basis with logical addition". Mathematical Notes of the Academy of Sciences of the USSR. 41 (4): 333–338. doi:10.1007/BF01137685.
  • Razborov, Alexander A. (May 1989). "On the method of approximations" (PDF. 1.41MB). Proceedings of the 21st Annual ACM Symposium on the Theory of Computing. Seattle, Washington, United States. pp. 167–176. doi:10.1145/73007.73023.
  • Razborov, A. A. (December 1990). "Lower bounds of the complexity of symmetric boolean functions of contact-rectifier circuits". Mathematical Notes of the Academy of Sciences of the USSR. 48 (6): 1226–1234. doi:10.1007/BF01240265.
  • Razborov, Alexander A.; Rudich, Stephen (May 1994). "Natural proofs" (PostScript). Proceedings of the 26th Annual ACM Symposium on the Theory of Computing. Montreal, Quebec, Canada. pp. 204–213. doi:10.1145/195058.195134.
  • Razborov, Alexander A. (December 1998). "Lower Bounds for the Polynomial Calculus" (PostScript). Computational Complexity. 7 (4): 291–324. doi:10.1007/s000370050013.
  • Razborov, Alexander A. (January 2003). "Propositional proof complexity" (PostScript). Journal of the ACM. 50 (1): 80–82. doi:10.1145/602382.602406. (Survey paper for JACM's 50th anniversary)

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