Title says it all, but in other words, does the length of the description of a Turing Machine also affect its complexity? Or is its complexity only affected by its running time?
An example of such a machine could be one that has a "branch" for each symbol of input in a tree: the first branch would be for the first symbol of input, then there would be a branch in both sides of the first branch for the second symbol of input, etc. This machine would run in linear time (one branch for every symbol), but it would have an exponential description ($2^n - 1$ states).