Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2206.05274

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

Nick Zhang
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

cs.GL

Keep this discovery

BibTeXRIS

Nick Zhang. 2022-06-12. 50 Years of Computational Complexity: Hao Wang and the Theory of Computation. https://arxiv.org/abs/2206.05274

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The Reconstructions of Konrad Zuse's Z3 Computer

This paper reviews the various reconstructions of Konrad Zuse's Z3 computer, built in 1941. The first is the reconstruction made by Zuse himself in the 1960s, which is now housed at the Deutsches Museum in Munich. Second is the 2001 reconstruction, made in Berlin, and which has a didactic purpose. Third is the Z3r, a Z3 reconstruction built by Horst Zuse in honor of his father's 100th birthday. Fourth is the reconstruction by Christoph Traber in Switzerland. All of these machines strive to preserve the cultural heritage that the Z3 represents.

cs.GL↗
arXiv2026

A Brief History of Fr\'echet Distances: From Curves and Probability Laws to FID

This note provides a chronological account of Fr\'echet distances, starting with Maurice Fr\'echet's 1906 doctoral thesis on distances in abstract sets and tracing the Fr\'echet distance between polygonal curves and its algorithmic computation in the 1990s. It then continues with his 1957 paper on a coupling-based distance between probability laws with a brief glimpse of Wasserstein distance and optimal transport. We further attempt to draw connections between the distributional, coupling-based facet of Fr\'echet distances on probability laws and the geometric facet on curves. The note ends with a modern use case, the Fr\'echet Inception Distance (FID) in the era of deep generative model evaluation, interpretable as the Wasserstein-2 distance between multivariate Gaussians in a learned feature space. An appendix includes \TeX{}ified faithful English translations of Fr\'echet's 1906 thesis and 1957 paper, and L\'evy's 1950 note for reader convenience.

cs.GL↗
arXiv2026

The Theorems of Dr. David Blackwell and Their Contributions to Artificial Intelligence

Dr. David Blackwell was a mathematician and statistician of the first rank, whose contributions to statistical theory, game theory, and decision theory predated many of the algorithmic breakthroughs that define modern artificial intelligence. This survey examines three of his most consequential theoretical results the Rao Blackwell theorem, the Blackwell Approachability theorem, and the Blackwell Informativeness theorem (comparison of experiments) and traces their direct influence on contemporary AI and machine learning. We show that these results, developed primarily in the 1940s and 1950s, remain technically live across modern subfields including Markov Chain Monte Carlo inference, autonomous mobile robot navigation (SLAM), generative model training, no-regret online learning, reinforcement learning from human feedback (RLHF), large language model alignment, and information design. NVIDIAs 2024 decision to name their flagship GPU architecture (Blackwell) provides vivid testament to his enduring relevance. We also document an emerging frontier: explicit Rao Blackwellized variance reduction in LLM RLHF pipelines, recently proposed but not yet standard practice. Together, Blackwell theorems form a unified framework addressing information compression, sequential decision making under uncertainty, and the comparison of information sources precisely the problems at the core of modern AI.

cs.GL↗