On the Work of Madhu Sudan: the 2002 Nevalinna Prize Winner

TL;DR

Madhu Sudan's influential work in computational complexity and coding theory includes key results like the probabilistic characterization of NP and a polynomial-time list decoding algorithm for Reed Solomon codes, significantly impacting theoretical computer science.

Contribution

The paper highlights Sudan's groundbreaking contributions to PCP theorem and list decoding, advancing understanding of NP verification and error correction.

Findings

Probabilistic characterization of NP class.

Polynomial-time list decoding algorithm for Reed Solomon codes.

Implications for complexity of approximation problems.

Abstract

Madhu Sudan's work spans many areas of computer science theory including computational complexity theory, the design of efficient algorithms, algorithmic coding theory, and the theory of program checking and correcting. Two results of Sudan stand out in the impact they have had on the mathematics of computation. The first work shows a probabilistic characterization of the class NP -- those sets for which short and easily checkable proofs of membership exist, and demonstrates consequences of this characterization to classifying the complexity of approximation problems. The second work shows a polynomial time algorithm for list decoding the Reed Solomon error correcting codes. This short note will be devoted to describing Sudan's work on probabilistically checkable proofs -- the so called {\it PCP theorem} and its implications.