Some Results on the Power of Nondeterministic Computation

11/04/2018

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by   Hiroki Morizumi, et al.

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In this paper, we consider the power of nondeterministic computation in two directions. In the first part of this paper, we consider nondeterministic computation and advice strings in bounded space computation. More precisely, we prove that L/quasipoly⊃NL/poly. As a corollary, we obtain that L/quasipoly⊃NL. In the proof, we show a relation between nondeterministic branching programs and bounded width Boolean circuits. In the second part of this paper, we consider the power of nondeterministic circuits. We prove that there is a Boolean function f such that the nondeterministic U_2-circuit complexity of f is at most 2n + o(n) and the deterministic U_2-circuit complexity of f is 3n - o(n).