50 Years of Computational Complexity: Hao Wang and the Theory of Computation

TL;DR

This paper reviews the 50-year history of computational complexity, highlighting Hao Wang's influential role and tracing its development from Turing's foundational work to Cook's complexity theory.

Contribution

It provides a historical overview emphasizing Hao Wang's contributions to the development of computational complexity theory.

Findings

Hao Wang significantly influenced early computational complexity research

The paper contextualizes the evolution of complexity theory over 50 years

It highlights the connection between Wang's work and modern complexity theory

Abstract

If Turing's groundbreaking paper in 1936 laid the foundation of the theory of computation (ToC), it is no exaggeration to say that Cook's paper in 1971, "The complexity of theorem proving procedures", [4] has pioneered the study of computational complexity. So computational complexity, as an independent research field, is 50 years old now (2021) if we date from Cook's article. This year coincides with the 100th birthday of Cook's mentor Hao Wang, one of the most important logicians. This paper traces the origin of computational complexity, and meanwhile, tries to sort out the instrumental role that Wang played in the process.