Abstract
In this paper, we consider the help bit problem in the decision tree model proposed by Nisan, Rudich and Saks (FOCS ’94). When computing k instances of a Boolean function f, Beigel and Hirst (STOC ’98) showed that⌊log2 k ⌋+ 1 help bits are necessary to reduce the complexity of f, for any function f, and exhibit the functions for which ⌊log2 k ⌋+ 1 help bits reduce the complexity. Their functions must satisfy the condition that their complexity is greater than or equal to k-1. In this paper, we show new functions satisfying the above conditions whose complexity are only 2√k. We also investigate the help bit problem when we are only allowed to use decision trees of depth 1. Moreover, we exhibit the close relationship between the help bit problem and the complexity for circuits with a majority gate at the top.
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© 2001 Springer-Verlag Berlin Heidelberg
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Amano, K., Hirosawa, T., Watanabe, Y., Maruoka, A. (2001). The Computational Power of a Family of Decision Forests. In: Sgall, J., Pultr, A., Kolman, P. (eds) Mathematical Foundations of Computer Science 2001. MFCS 2001. Lecture Notes in Computer Science, vol 2136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44683-4_12
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DOI: https://doi.org/10.1007/3-540-44683-4_12
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