this article, we are interested in characterizing as precisely as possible, those problems that can and cannot be solved by a computer. We are not concerned here with the efficiency or practicality of the solutions; we are merely interested in any computer solution to the problem, even one that is unrealistically slow or that operates on an imaginary computer, even one exploiting unbounded time and memory space. The equally important problem of characterizing the problems that can and cannot be computed efficiently is addressed elsewhere in this encyclopedia. See Computational Complexity Theory.