  In this paper, we consider a new direction of computation, which we call
computation with large advice. We mainly consider constant space computation
with large advice in Turing machines, and prove the following facts: (i) The
class of decision problems solvable by a constant space Turing machine with
polynomial-size advice includes nonuniform-{\sf NC}$^1$, (ii) The class of
decision problems solvable by a constant space Turing machine with
quasipolynomial-size advice equals nonuniform-{\sf polyL}. The facts mean
constant space computation with large advice has unexpected computational
power. On the other hand, we mention bounded time computation with large
advice, and attempt to propose a concept of ``algorithms with large advice''.
In the proposal, advice is precomputed data for a problem and a fixed instance
size, and we expect efficient algorithms by large or huge advice.
