I'm currently trying to prove a language regular (for personal amusement). The language is:
The language containing all numbers in ternary that have even bit-parity when encoded in binary.
Now, I've currently tried a few different approaches that have not led me to any success. I've tried using the pumping lemma (couldn't find anything to pump on), Myhill-Nerode (similar) and even counted the number of strings of each length for which the statement is true (my intuition is that it checks out with a probabilistic argument).
Are their any other approaches that might help here, or are there any intuitions that might be helpful? At this point, my best guess is that the language is not regular, but I don't seem to be able to come up with an explanation.