We study the relationship between standard alphabets over the equality atoms, and those which can be made homogeneous using finitely many relations and functions. We leave open the problem whether these notions coincide.

# Category Archives: open problems

# A conjecture concerning Brzozowski algorithm (PRIZE!)

Fix attention on equality atoms.

Given an orbit-finite, deterministic automaton on the alphabet of atoms, a *Brzozowski phase* amounts to:

- reversing the direction of all transition arrows and swapping initial and accepting states,
- determinising the result, and
- cutting to the reachable part.

# Least supports and the representation theorem

This post discusses equivalence of:

1. existence of the least supports

2. representation theorem