Explicit lower bound of 4.5n - o(n) for boolena circuits

Lachish, Oded and Raz, R. (2001) Explicit lower bound of 4.5n - o(n) for boolena circuits. In: Vitter, J.S. and Spirakis, P. and Yannakakis, M. (eds.) STOC '01: Proceedings of the thirty-third annual ACM symposium on Theory of computing. Association for Computing Machinery, pp. 399-408. ISBN 9781581133493.

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Official URL: https://doi.org/10.1145/380752.380832

Abstract

We prove a lower bound of 4.5n - o(n) for the circuit complexity of an explicit Boolean function (that is, a function constructible in deterministic polynomial time), over the basis U_2. That is, we obtain a lower bound of 4.5n - o(n) for the number of {and,or} gates needed to compute a certain Boolean function, over the basis {and,or,not} (where the not gates are not counted). Our proof is based on a new combinatorial property of Boolean functions, called Strongly-Two-Dependence, a notion that may be interesting in its own right. Our lower bound applies to any Strongly-Two-Dependent Boolean function.

Metadata

Item Type:	Book Section
School:	Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
Depositing User:	Sarah Hall
Date Deposited:	25 May 2021 14:05
Last Modified:	09 Aug 2023 12:50
URI:	https://eprints.bbk.ac.uk/id/eprint/44415

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