Exact constant for constant‑size undecidable levels

Ascertain the smallest constant level size sufficient to encode undecidable instances via a universal counter machine in each of the games proved RE‑complete in this paper, thereby identifying exact constants for constant‑size level undecidability.

Background

Using universal counter machines, the authors show undecidability even for constant‑size levels and give an explicit single‑screen construction in New Super Mario Bros. Wii. They note, however, that the minimal constant required is not determined.

They suggest further compacting constructions and exploring whether similarly small universal counter machines can fit within Super Mario Maker’s standard level size constraints.