Realistic, modern-day computers are limited by the soft limits of computation. Theoretical computers, like the Turing Machine, are limited by the hard limits of computation.
Soft Limits Of Computation
Cobham’s Thesis, which defines the tractability of a problem, is considered to be the soft limits of computation. No traditional methods of computation can solve intractable problems (problems with ),
However, using randomised heuristics such as Simulated Annealing or Machine Learning algorithms, it is possible to to obtain an approximate, ‘good-enough’ solution.
Hard Limits Of Computation
The hard limits of computation refers to computers’ inability to solve incomputable problems. No matter how advanced a computer can get, the Church-Turing Thesis shows that some undecidable and incomputable problems exist, that can never be solved.