An Introduction to Computational Complexity Via Games
Bibliographic record
Abstract
In this talk I will discuss an approach to solving the famous P=NP question using games. For those unfamiliar with computational complexity, I will describe the complexity classes P and NP, as well as a few other complexity classes, including coNP, L and NL. I will then describe the million-dollar problem that asks whether P=NP and show how one can use a classic two-person combinatorial game, known as an Ehrenfeucht-Fraisse game (along with its relatives), to try to separate complexity classes. I will give some simple examples of how these games are played and then describe a newly rediscovered game that my colleagues and I at IBM are exploring that are potentially more powerful than these classical games. About the Speaker: Jon is a member of the research staff at the IBM T.J. Watson Research Center in New York. Jon has been with IBM for the last 25 years. Along with several colleagues, he developed the strategy component of the IBM Watson Jeopardy-playing system that in 2011 defeated the two most successful human Jeopardy players on live television. He has built two commercial robots and worked with the Toronto Raptors of the National Basketball Association on a system to help with trades and draft picks. From 2016-2018 Jon was the chief scientist of IBM’s two African research labs, one in Nairobi, Kenya, and the other in Johannesburg, South Africa. Since returning from Africa, Jon’s work has focused on applications of mathematical logic to theoretical questions in computer science, like the P=NP question. This is an in-person talk also available via Zoom.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.002 | 0.009 |
| Scholarly communication | 0.006 | 0.013 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.003 | 0.010 |
| Insufficient payload (model declined to judge) | 0.019 | 0.004 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".