Computation with Large Advice

02/12/2023

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by   Hiroki Morizumi, et al.

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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-NC^1, (ii) The class of decision problems solvable by a constant space Turing machine with quasipolynomial-size advice equals nonuniform-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.