Category Archives: students

Screenshot 2023-05-16 at 8.36.51 PM

Math 100 student’s protein folding research

Madison Koskey had the highest score in the class on this project task:

Fold an idealized protein known as S64 to obtain a highest possible score in the hydrophobic-polar protein folding model in three dimensions.

This problem was studied by Lesh, Mitzenmacher, and Whitesides (2003).

Above we see Madison’s intricate folding of S64 which earned a score of 27.

To try your hand at rotating it in 3D, go directly to this link.

Slides for October 30


The number of languages with maximum state complexity

Lei Liu completed her Master’s degree with the project title Complexity of Options in 2017.
An extension to monotone options (pictured) was presented at
ALH-2018. The new paper is called The number of languages with maximum state complexity and has been accepted for TAMC 2019.

As of 2022, the paper has been through 7 revisions and has been accepted for publication in the journal Algebra Universalis.

Some of the 168 monotone Boolean functions of 4 variables

Studio_Project (6)

Master’s projects in Lean

After Jake Fennick’s MA project in the proof assistant Isabelle in 2019, I have advised two Master’s students whose project focused on another popular proof assistant, Lean:
  • Hugh Chou, 2021: Formalizing my paper on a conflict in the Carmo and Jones approach to contrary-to-duty deontic obligations.
  • Ryan T. Sasaki, 2022: Formalizing a time-invariance theorem for Redington immunization in financial mathematics.

Humuhumunukunukuapua’a at the Symposium

2nd Annual SURE Symposium 2019

SURE: Summer Undergraduate Research Experience

will feature two projects mentored by Prof. Kjos-Hanssen:

VC-dimensions of nondeterministic finite automata for words of equal length

Davin Takahashi and Ethan Lamb

Ishigami and Tani studied VC-dimensions of finite automata. We show that their results apply to a new notion, lower VC-dimension, where all sets (instead of some set) of a given cardinality must be shattered. We also relate the VC-dimension to the Separating Words problem.

Savings from word powers in automatic complexity

Sun Young Kim and Clyde Felix

The automatic complexity of a word was introduced by Shallit and Wang in 2001 and studied further by Kjos-Hanssen since 2013. In this work we develop an implementation of a lower bound on the complexity involving occurrences of powers of words, such as the occurrence of “humu” twice in “humuhumunukunukuapua’a”.


The Complexity Option Game

2014 M.A. graduate Malihe Alikhani completed her Master’s project on American option pricing and optimal stopping for success runs. She participated in the Cornell Summer School in Probability 2014.

Her project constitutes one of the parts of the new paper Pricing Complexity Options, which appeared in
Algorithmic Finance, 2015.

Entry at IOS Press

The best version of the paper is at

The ideas are implemented in the Complexity Option Game!