# László Babai

László Babai
László Babai at Oberwolfach in 2011
BornJuly 20, 1950 (age 72)
NationalityHungarian
AwardsGödel Prize (1993)
Knuth Prize (2015)
Dijkstra Prize (2016)
Scientific career
FieldsComputer Science, Mathematics
InstitutionsUniversity of Chicago
Vera T. Sós
Doctoral studentsMario Szegedy
Gábor Tardos

László "Laci" Babai (born July 20, 1950, in Budapest)[1] is a Hungarian professor of computer science and mathematics at the University of Chicago. His research focuses on computational complexity theory, algorithms, combinatorics, and finite groups, with an emphasis on the interactions between these fields.

## Life

In 1968, Babai won a gold medal at the International Mathematical Olympiad. Babai studied mathematics at Faculty of Science of the Eötvös Loránd University from 1968 to 1973, received a Ph.D. from the Hungarian Academy of Sciences in 1975, and received a D.Sc. from the Hungarian Academy of Sciences in 1984.[1][2] He held a teaching position at Eötvös Loránd University since 1971; in 1987 he took joint positions as a professor in algebra at Eötvös Loránd and in computer science at the University of Chicago. In 1995, he began a joint appointment in the mathematics department at Chicago and gave up his position at Eötvös Loránd.[1]

## Work

He is the author of over 180 academic papers.[1] His notable accomplishments include the introduction of interactive proof systems,[3] the introduction of the term Las Vegas algorithm,[4] and the introduction of group theoretic methods in graph isomorphism testing.[4] In November 2015, he announced a quasipolynomial time algorithm for the graph isomorphism problem.[5][6]

He is editor-in-chief of the refereed online journal Theory of Computing.[7] Babai was also involved in the creation of the Budapest Semesters in Mathematics program and first coined the name.

### Graph isomorphism in quasipolynomial time

After announcing the result in 2015,[6][8][9] Babai presented a paper proving that the graph isomorphism problem can be solved in quasi-polynomial time in 2016, at the ACM Symposium on Theory of Computing.[10] In response to an error discovered by Harald Helfgott, he posted an update in 2017.[11]

abstract

We show that the Graph Isomorphism (GI) problem and the related problems of String Isomorphism[12] (under group action) (SI) and Coset Intersection (CI)[13][14] can be solved in quasipolynomial ${\displaystyle \exp \left(\left(\log n\right)^{O\left(1\right)}\right)}$ time. The best previous bound for GI was ${\displaystyle \exp \left(O\left({\sqrt {n\log n}}\right)\right),}$ where ${\displaystyle n}$ is the number of vertices (Luks, 1983); for the other two problems, the bound was similar, ${\displaystyle \quad \qquad \exp \left({\tilde {O}}\left({\sqrt {n}}\right)\right),}$ where ${\displaystyle n}$ is the size of the permutation domain (Babai, 1983).
The algorithm builds on Luks's SI framework and attacks the barrier configurations for Luks's algorithm by group theoretic «local certificates» and combinatorial canonical partitioning techniques. We show that in a well-defined sense, Johnson graphs are the only obstructions to effective canonical partitioning.

## Honors

In 1988, Babai won the Hungarian State Prize, in 1990 he was elected as a corresponding member of the Hungarian Academy of Sciences, and in 1994 he became a full member.[1] In 1999 the Budapest University of Technology and Economics awarded him an honorary doctorate.[1]

In 1993, Babai was awarded the Gödel Prize together with Shafi Goldwasser, Silvio Micali, Shlomo Moran, and Charles Rackoff, for their papers on interactive proof systems.[15]

In 2015, he was elected[16] a fellow of the American Academy of Arts and Sciences, and won the Knuth Prize.

Babai was an invited speaker at the International Congresses of Mathematicians in Kyoto (1990), Zürich (1994, plenary talk), and Rio de Janeiro (2018).

## Sources

copy from Lenta.ru // texnomaniya.ru, 20 ноября 2015
Опубліковано швидкий алгоритм для задачі ізоморфізму графів Archived 2017-07-03 at the Wayback Machine // Джерело: Хабрахабр, перекладено 16 грудня 2015, 06:30

## References

1. Curriculum vitae from Babai's web site, retrieved 2016-01-28.
2. ^
3. ^ Babai, László; Moran, Shlomo (1988), "Arthur-Merlin games: a randomized proof system, and a hierarchy of complexity class", J. Comput. Syst. Sci., 36 (2): 254–276, doi:10.1016/0022-0000(88)90028-1.
4. ^ a b Babai, László (1979), Monte-Carlo algorithms in graph isomorphism testing (PDF), Tech. Report, Université de Montréal.
5. ^ Cho, Adrian (November 10, 2015), "Mathematician claims breakthrough in complexity theory", Science, doi:10.1126/science.aad7416
6. ^ a b Klarreich, Erica (14 December 2015). "Landmark Algorithm Breaks 30-Year Impasse". quantamagazine.org. Quanta Magazine.
7. ^ Theory of Computing editors, retrieved 2010-07-30.
8. ^ A Big Result On Graph Isomorphism // November 4, 2015, A Fast Graph Isomorphism Algorithm // November 11, 2015
9. ^ Claimed Breakthrough Slays Classic Computing Problem // MIT Technology Review, by Tom Simonite on November 13, 2015
10. ^ Babai, László (2016), "Graph Isomorphism in Quasipolynomial Time [Extended Abstract]", Proceedings of the Forty-Eighth Annual ACM Symposium on Theory of Computing (STOC '16), New York, NY, USA: ACM, pp. 684–697, arXiv:1512.03547, doi:10.1145/2897518.2897542, ISBN 978-1-4503-4132-5, S2CID 17118954
11. ^ László Babai: Fixing the UPCC case of Split-or-Johnson, posted on 14 January 2017
12. ^ Definition 2.3. String Isomorphism, in: Transactions on Computational Science V. Special Issue on Cognitive Knowledge Representation. Editors-in-Chief: Marina L. Gavrilova, C. J. Kenneth Tan. Editors: Yingxu Wang, Keith Chan / Lecture Notes in Computer Science / Volume 5540, Springer Verlag, 2009
13. ^
14. ^ Complexity of the coset intersection problem // Theoretical Computer Science Stack Exchange, asked Sep 25 2014 at 9:43
15. ^ 1993 Gödel Prize Archived 2015-12-08 at the Wayback Machine, ACM SIGACT, retrieved 2010-08-14.
16. ^