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• W2000356135 abstract "Combinational complexity and depth are the most important complexity measures for Boolean functions. It has turned out to be very hard to prove good lower bounds on the combinational complexity or the depth of explicitly defined Boolean functions. Therefore one has restricted oneself to models where nontrivial lower bounds are easier to prove. Here decision trees, branching programs, and one-time-only branching programs are considered, where each variable may be tested on each path of computation only once. Efficient algorithms for the construction of optimal decision trees and optimal one-time-only branching programs for symmetric Boolean functions are presented. Furthermore, the following trade-off results are proved. An exponential lower bound on the decision tree complexity of some Boolean function is shown having linear formula size and linear one-time-only branching program complexity. Furthermore, a quadratic lower bound on the one-time-only branching program complexity of some Boolean function is shown having linear combinational complexity." @default.
• W2000356135 created "2016-06-24" @default.
• W2000356135 creator A5075262791 @default.
• W2000356135 date "1984-08-01" @default.
• W2000356135 modified "2023-09-27" @default.
• W2000356135 title "Optimal decision trees and one-time-only branching programs for symmetric Boolean functions" @default.
• W2000356135 cites W2011918838 @default.
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• W2000356135 doi "https://doi.org/10.1016/s0019-9958(84)80031-5" @default.
• W2000356135 hasPublicationYear "1984" @default.
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