Progress in computational complexity theory

Authors:
Jin-Yi Cai;Hong Zhu
Affiliations:
Computer Sciences Department, University of Wisconsin, Madison, WI and Tsinghua University, Beijing, P.R. China;Computer Sciences Department, Fudan University, Shanghai, P.R. China
Venue:
Journal of Computer Science and Technology
Year:
2005

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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.