I have two questions as in the title:
- TM M accepts some string of length greater than 100
- TM M accepts some string of length at most 100
Since 1. is infinite, we can rephrase question as "does TM accept a string", which is clearly undecidable and there are many proofs for that.
2nd question on the other hand is finite and all finite languages are decidable.
Is my reasoning correct? I can't find any confirmation of my theories.