Summary
The k-th threshold function, T nk , is defined as: \(T_k^n \left( {x_1 ,...,x_n } \right) = \left\{ \begin{gathered} 1 if \sum\limits_{i = 1}^n {x_i \geqq k} \hfill \\ 0 otherwise \hfill \\ \end{gathered} \right.\) where x iε{0,1} and the summation is arithmetic. We prove that any monotone network computing T 3/n(x 1,...,x n) contains at least 2.5n-5.5 gates.
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Blum, N.: A Boolean Function Requiring 3n Network Size. Theor. Comput. Sci. 28, 337–345 (1984)
Bloniarz, P.: The Complexity of Monotone Boolean Functions and an Algorithm for Finding Shortest Paths in a Graph. Ph.D. Dissertation, Techn. Rep. No. 238. Lab. Comput. Sci M.I.T (January 1979)
Dunne, P.E.: Lower Bounds on the Monotone Network Complexity of Threshold Functions. In: Proceedings of 22nd Annual Allerton Conf. On Communication, Control and Computing, pp. 911–920 (October 1984)
Mehlhorn, K., Galil, Z.: Monotone Switching Networks and Boolean Matrix Product. Computing 16, 99–111 (1976)
Paterson, M.S.: An Introduction to Boolean Function Complexity. Tech. Rep. Dept. Comput. Sci., Stanford, STAN-CS-76-557 (1976)
Tiekenheinrich, J.: A 4n-Lower Bound on the Monotone Network Complexity of a One-Output Boolean Function. Inf. Process. Lett. 18, 201–202 (1984)
Wegener, I.: Boolean Functions Whose Monotone Complexity is of Size n2/log n. Theor. Comput. Sci. 21, 213–224 (1982)
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This research was supported by the Science and Engineering Research Council of Great Britain, UK
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Dunne, P.E. A 2.5n lower bound on the monotone network complexity of T3n. Acta Informatica 22, 229–240 (1985). https://doi.org/10.1007/BF00264232
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DOI: https://doi.org/10.1007/BF00264232