Computation with Large Advice

Abstract: 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.