Lower bounds for linear decision trees with bounded weights

Kei Uchizawa, Eiji Takimoto

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

1 被引用数 (Scopus)

抄録

In this paper, we consider a linear decision tree such that a linear threshold function at each internal node has a bounded weight: the sum of the absolute values of its integer weights is at most w. We prove that if a Boolean function f is computable by such a linear decision tree of size (i.e., the number of leaves) s and rank r, then f is also computable by a depth-2 threshold circuit containing at most s(2w+1)r threshold gates with weight at most (2w+1)r+1 in the bottom level. Combining a known lower bound on the size of depth-2 threshold circuits, we obtain a 2Ω(n/ logw) lower bound on the size of linear decision trees computing the Inner-Product function modulo 2, which improves on the previous bound 2√n if w = 2o(√n).

本文言語英語
ホスト出版物のタイトルSOFSEM 2015
ホスト出版物のサブタイトルTheory and Practice of Computer Science - 41st International Conference on Current Trends in Theory and Practice of Computer Science,
編集者Giuseppe F. Italiano, Tiziana Margaria-Steffen, Jaroslav Pokorný, Jean-Jacques Quisquater, Roger Wattenhofer
出版社Springer Verlag
ページ412-422
ページ数11
ISBN(電子版)9783662460771
DOI
出版ステータス出版済み - 1 1 2015
イベント41st International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2015 - Pec pod Sněžkou, チェコ共和国
継続期間: 1 24 20151 29 2015

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
8939
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

その他

その他41st International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2015
Countryチェコ共和国
CityPec pod Sněžkou
Period1/24/151/29/15

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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