Abstract
Revealing the power of nondeterministic computation and co-nondeterministic computation is one of the central problems in computational complexity. In this paper, we consider the two computation and deterministic computation in Boolean circuits. We give the first separations on the power of deterministic circuits, nondeterministic circuits, and co-nondeterministic circuits in general circuits. More precisely, we prove the following facts.
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There is an explicit Boolean function f such that the nondeterministic \(U_2\)-circuit complexity of f is at most \(2n + o(n)\) and the deterministic and co-nondeterministic \(U_2\)-circuit complexity of f is \(3n - o(n)\).
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There is an explicit Boolean function f such that the co-nondeterministic \(U_2\)-circuit complexity of f is at most \(2n + o(n)\) and the deterministic and nondeterministic \(U_2\)-circuit complexity of f is \(3n - o(n)\).
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The author would like to thank the anonymous reviewers for valuable and detailed comments.
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Morizumi, H. (2021). On the Power of Nondeterministic Circuits and Co-Nondeterministic Circuits. In: Leporati, A., MartÃn-Vide, C., Shapira, D., Zandron, C. (eds) Language and Automata Theory and Applications. LATA 2021. Lecture Notes in Computer Science(), vol 12638. Springer, Cham. https://doi.org/10.1007/978-3-030-68195-1_9
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DOI: https://doi.org/10.1007/978-3-030-68195-1_9
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