Minimality of signature automata by merging top-level equivalence classes

Determine whether a minimal deterministic parity automaton recognising a positional language can be obtained from a signature automaton by merging ≈_d-equivalent states (i.e., whether this yields a canonical minimal form).

Background

Signature automata encode layered preorders. The authors observe they may not be minimal and conjecture that merging the top-level equivalence classes could always yield a minimal automaton, hinting at a potential canonical form and a pathway to efficient minimisation.