(updated - more formal, removed some parts and improved general clarity)
Over years, I come again and again back to Halting Problem and it's
unsolvability ..now I have created a system, which is theoretically
able to find halting problems in far larger class of systems than just
FSM's.
It's based on what I call topological
identicalness of abstractions and abstraction of programs - it could, basically, prove
somewhat different programs identical if they follow the same logic. It
is not meant to be runnable on normal computer - it takes a lot of
memory. It's, right now, a pure theory. When it's ready as theory, it