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.

Service and administration

Some recent departmental service I have enjoyed being involved in includes:
  • Associate Chair (since 2021)
  • Personnel committee chair (2020-2021)
  • Hiring committee chair (2019-2020)
There are a couple of items under service to the profession as well:
  • Editor, Journal of Logic and Analysis (since 2019)
  • Moderator, CS Theory Stack Exchange (since 2018)

MATH 654 Fall 2022

Watch this space for updates on logic courses.

The undergraduate course MATH 454 (Axiomatic Set Theory) was taught in Fall 2021. Textbook: Schimmerling’s “A course on set theory”

A similar course at the graduate level was MATH 654 Fall 2020, which had the following readings:

  • Foundations of Mathematics, Kenneth Kunen, parts of chapters I-IV.
  • Modal logic for open minds, Johan van Benthem, some of chapters 1-11 and 16.
  • Logic and Proof, Lean tutorial, and The Natural Number Game

Math 654 in Fall 2022 will use the textbook by Ebbinghaus, Flum, and Thomas and some readings about Lean.


Recent CiE papers

Three new papers

with graduate students Birns (left) and Webb (right).
  1. KL-randomness and effective dimension under strong reducibility (with David J. Webb). Computability in Europe, Lectures Notes in Computer Science, 2021.
  2. On the degrees of constructively immune sets (with Samuel D. Birns). Computability in Europe, Lectures Notes in Computer Science, 2021.
  3. Strong Medvedev reducibilities and the KL-randomness problem (with David J. Webb). Computability in Europe, Lectures Notes in Computer Science, 2022.

Principles-based classification

I was the discussant for the following paper at Hawaii Accounting Research Conference 2020 on the UH Hilo campus:

The Contract Disclosure Mandate and Earnings Management under External Scrutiny

by Carlos Corona and Tae-Wook Ryan Kim

Discussant slides

I learned that research in the Theory Track of the accounting discipline primarily is about mathematical modeling of the effects of government policies and business decisions. It borrows methods from economics for such modeling. In the case of the Corona-Kim paper: quadratic programming without constraints, and exponential utility functions. Usually these are not empirical papers, i.e., they don’t test the model explicitly against data. Indeed this would be hard to do with notions like “intensity of scrutiny”.

I am a discussant for “A theory of principles-based classification” by Konvalinka, Penno, and Stecher, at HARC 2021.