Automatic Complexity 2014-2019

The Simons Foundation under the program Collaboration Grants for Mathematicians (#315188 to Bjørn Kjos-Hanssen, grant title “Automatic Complexity”) supported my travel during 2014–2019.

Year Trips
2014 – 2015 COCOA 2014 (Maui); U. Washington; Varieties of Algorithmic Information; CCR, Heidelberg; Haidar to Arizona Winter School
2015 – 2016 ASL Annual Meeting, UConn (myself and Beros); SIAM Meeting on Discrete Math, Atlanta
2016 – 2017 WoLLIC, London; UCNC, Arkansas
2017 – 2018 Workshop on Computability Theory, Waterloo
2018 – 2019 Computability Theory and Foundations of Mathematics, Tokyo; Joint Math Meetings, Baltimore

Nine subprojects

Here are papers produced about automatic complexity, many with Master’s students.
Conferences in parentheses are those with no published proceedings.
Students or consultants in parentheses discussed the topic but were not coauthors.

Student/consultant Conference Journal
Hyde (MA, 2013) COCOON 2014 Elec. J. Combinatorics (2015)
COCOA 2014 Theoretical Computer Science (2015)
Alikhani (MA, 2014); Pakravan, Saadat (MSc Fin.Eng., 2013) Algorithmic Finance (2015)
(written at CCR 2015) Theory of Computing Systems (2017)
(Castiglione 2015) WoLLIC 2017 Discrete Mathematics (2018)
(Kobayashi 2016) (VAI 2015) Experimental Mathematics (2019)
(Huggins 2016) UCNC 2017
Liu (MA, 2017) (ALH 2018)
Yogi (MA, 2018)

For instance, I gave a talk in the Seattle Probability Seminar organized by Soumik Pal and Chris Burdzy at the University of Washington Department of Mathematics.

Kolmogorov structure functions for automatic complexity


We study an analogue of Kolmogorov’s notion of structure function, introduced in 1973, with Kolmogorov complexity replaced by Shallit and Wang’s (2001) automatic complexity. We discuss the prospects for using it for model selection in statistics. We prove an upper bound which is piecewise smooth, related to the binary entropy function, and appears to be fairly sharp based on numerical evidence.

The paper is loosely coupled with the following software:
- Complexity Guessing Game
- Complexity Option Game
- Structure Function Calculator
These are gathered in some slides.com slides.