Category Archives: students


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”.


TAMC 2019: 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.

Some of the 168 monotone Boolean functions of 4 variables


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!


Graduate Program in Logic

The Department of Mathematics at University of Hawaii at Manoa has long had an informal graduate program in logic, lattice theory, and universal algebra going back to Alfred Tarski’s student William Hanf.
Starting in 2016, things are getting a little more formal.

We intend the following course rotation (repeating after two years):

Semester Course number Course title
Fall 2015 MATH 649B Graduate Seminar
Spring 2016 MATH 649* Applied Model Theory
Fall 2016 MATH 654* Graduate Introduction to Logic
Spring 2017 MATH 657 Computability and Complexity

*Actual course numbers may vary.

Faculty who may teach in the program

David A. Ross, Professor
Bjørn Kjos-Hanssen, Professor
Mushfeq Khan, Temporary Assistant Professor 2014-2017
Achilles Beros, Temporary Assistant Professor 2015-2017