In Dhruv's GRECS wiki, http://grecs.wikispaces.com/ , there is a TM question "Will this TM finish computing before sunset if it were to start before sunrise on the same day? ", which is said to be undecidable. I think the sentence is equivalent to " Will this TM accept a certain string within 'k' steps?" And I guess it's decidable, since it's very like "Will a TM halt within 'k' steps?" ,and maybe it's a subset of this one.
The expression like "before sunset" which emphasizes time rather than "steps" is weird. Most of the textbooks and questions use "steps", since every step definied in a TM is a limited number of actions that can be done within a given time, which implies that "time" is equivalent to "step" in a sense.
I've talked to Dhruv, and we want to get help from urch and experts. Just as he said, the CSGRE is notorious for asking questions that are slightly different from the ones you may already have encountered.
So, "Will this TM finish computing before sunset if it were to start before sunrise on the same day? ", decidable or undecidable?