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Journal of Computer Science and Technology

, Volume 20, Issue 6, pp 735–750 | Cite as

Progress in Computational Complexity Theory

  • Jin-Yi Cai
  • Hong Zhu
Article

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.

Keywords

theoretical computer science computational complexity theory PCP theorem inapproximability logspace complexity Reingold's theorem GAP problem primality testing complexity of lattice problems worst-case to average-case reductions pseudorandomness extractors holographic algorithms 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Computer Sciences DepartmentUniversity of WisconsinMadisonU.S.A.
  2. 2.Tsinghua UniversityBeijingP.R. China
  3. 3.Computer Sciences DepartmentFudan UniversityShanghaiP.R. China

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