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Progress in Computational Complexity Theory

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Abstract

We briefly survey a number of important recent achievements in Theoretical Computer Science (TCS), especially Computational Complexity Theory. We will discuss the PCP Theorem, its implications to inapproximability on combinatorial optimization problems; space bounded computations, especially deterministic logspace algorithm for undirected graph connectivity problem; deterministic polynomial-time primality test; lattice complexity, worst-case to average-case reductions; pseudorandomness and extractor constructions; and Valiant's new theory of holographic algorithms and reductions.

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Authors and Affiliations

  1. Computer Sciences Department, University of Wisconsin, Madison, WI, 53706, U.S.A.

    Jin-Yi Cai

  2. Tsinghua University, Beijing, 100084, P.R. China

    Jin-Yi Cai

  3. Computer Sciences Department, Fudan University, Shanghai, 200433, P.R. China

    Hong Zhu

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  1. Jin-Yi Cai
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Correspondence to Jin-Yi Cai.

Additional information

Supported by the NSF, USA (Grant Nos. CCR-0208013 and CCR-0511679) and the National Natural Science Foundation of China (Grant No. 60496321).

Jin-Yi Cai studied at Fudan University, Temple University and Cornell University, where he received his Ph.D. degree in 1986. He held faculty positions at Yale University (1986–1989), Princeton University (1989–1993), and SUNY Buffalo (1993–2000), rising from assistant professor to professor. He is currently a professor of computer science at the University of Wisconsin–Madison. He received a Presidential Young Investigator Award in 1990, an Alfred P. Sloan Fellowship in Computer Science in 1994, a John Simon Guggenheim Fellowship in 1998, and a Morningside Silver Medal of Mathematics in 2004. He also received the Humboldt Research Award for Senior U.S. Scientists. He has been elected a fellow of ACM.

Hong Zhu studied at Mathematical Department of Fudan University in 1956–1961, after graduated he became a teacher (from assistant professor to professor and surpervisor of Ph.D. candidates) of Fudan University since 1961. Hong Zhu works in the area of Theoretical Computer Science since 1978. He has two pieces of work cited by Knuth in his well known book, The Art of Computer Programming. He was a visiting professor of Clermont-Ferrand University and the University of North Carolina at Charlotte and the Advance Science and Technology University of Japan, etc. He is a joint professor of Shanghai Jiaotong University.

Hong Zhu serves as Syndic of Chinese Cryptology Society, Chairman of Association of Discrete Mathematics and on the Editorial Board of Computer and Artificial Intelligence (Europe).

Hong Zhu received a second rank award of Education Ministry for Progress in Science and Technology in 1997.

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Cai, JY., Zhu, H. Progress in Computational Complexity Theory. J Comput Sci Technol 20, 735–750 (2005). https://doi.org/10.1007/s11390-005-0735-4

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