I'm learning about time and space complexity involving Turing Machines at the moment, and would really like some concrete examples of specific languages that belong (or don't belong) to certain classes of time / space hierarchies. For example, what are some examples of a decidable language that can't be decided by a TM using space O(log n) and time less than n, on inputs of length n?
Might the Travelling Salesman Problem be an example to the above question, since I think the brute-force algorithm for TSP would take space O(n) (store the current shortest path, and compare it with each new path that's being explored)?