Documents
Thoughts
My current projects all have to do with deriving Kleene-style theorems for different flavours of automata, and using them to prove completeness results. At the moment, of particular interest is Guarded Kleene Algebra with Tests (GKAT), whose rather elegant theory was initiated in this paper from 2019. In that paper, a certain Uniqueness of Solutions axiom for GKAT is assumed, but it is also left open whether the axiom actually depends on the other GKAT axioms. I am hoping to resolve this issue.
Next on the list is an open problem attributed to Robin Milner. In a paper from 1984, Milner gave a sound axiomatisation of bisimulation equivalence for regular expressions. However, he left completeness as an open problem. This problem is still open, despite over 35 years of intelligent and intensive research (see this paper by Clemens Grabmeyer and Wan Fokkink for a partial solution to the problem as well as a historical overview). I think this problem is really interesting, and that the research that has gone into it could benefit from a more coalgebra-centric approach.
Aside from the projects listed above, I also have some interest in automated proof-writing and combinatorics (although I am not an expert in either).
All of the above put together, I occasionally have thoughts that would make good blog posts but not good papers. Since I don't actually care to have a real blog, these can be found below.