On the relationship between energy complexity and other boolean function measures
文献类型：期刊论文
| 作者 | Sun, Xiaoming1,2; Sun, Yuan1,2; Wu, Kewen3; Xia, Zhiyu1,2 |
| 刊名 | JOURNAL OF COMBINATORIAL OPTIMIZATION
 |
| 出版日期 | 2021-01-07 |
| 页码 | 23 |
| 关键词 | Energy complexity Decision tree Boolean function Circuit complexity |
| ISSN号 | 1382-6905 |
| DOI | 10.1007/s10878-020-00689-8 |
| 英文摘要 | We focus on energy complexity, a Boolean function measure related closely to Boolean circuit design. Given a circuit C over the standard basis {boolean OR(2), Lambda(2), (sic)}, the energy complexity of C, denoted by EC(C), is the maximum number of its activated inner gates over all inputs. The energy complexity of a Boolean function f, denoted by EC(f), is the minimum of EC(C) over all circuits C computing f. Recently, K. Dinesh et al. (International computing and combinatorics conference, Springer, Berlin, 738-750, 2018) gave EC(f) an upper bound by the decision tree complexity, EC(f) = O(D(f)(3)). On the input size n, They also showed that EC(f) is at most 3n - 1. For the lower bound side, they showed that EC(f) >= 1/3 psens(f), where psens(f) is called positive sensitivity. A remained open problem is whether the energy complexity of a Boolean function has a polynomial relationship with its decision tree complexity. Our results for energy complexity can be listed below. - For the lower bound, we prove the equation that EC(f) = Omega(root D(f)), which answers the above open problem. - For upper bounds, EC(f) <= min{1/2 D(f)(2) + O(D(f)), n + 2D(f) - 2} holds. - For non-degenerated functions, we also provide another lower bound EC(f) = Omega(log n) where n is the input size. - We also discuss the energy complexity of two specific function classes, OR functions and ADDRESS functions, which implies the tightness of our two lower bounds respectively. In addition, the former one answers another open question in Dinesh et al. (International computing and combinatorics conference, Springer, Berlin, 738-750, 2018) asking for non-trivial lower bound for energy complexity of OR functions. |
| 资助项目 | National Natural Science Foundation of China[61433014] ; National Natural Science Foundation of China[61832003] ; National Natural Science Foundation of China[61761136014] ; National Natural Science Foundation of China[61872334] ; National Natural Science Foundation of China[61502449] ; National Natural Science Foundation of China[61602440] ; National Natural Science Foundation of China[61801459] ; 973 Program of China[2016YFB1000201] ; K. C. Wong Education Foundation |
| WOS研究方向 | Computer Science ; Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000605896800003 |
| 出版者 | SPRINGER |
| 源URL | [http://119.78.100.204/handle/2XEOYT63/16371]  |
| 专题 | 中国科学院计算技术研究所期刊论文_英文 |
| 通讯作者 | Sun, Yuan |
| 作者单位 | 1.Chinese Acad Sci, Inst Comp Technol, CAS Key Lab Network Data Sci & Technol, Beijing, Peoples R China 2.Univ Chinese Acad Sci, Beijing, Peoples R China 3.Peking Univ, Sch Elect Engn & Comp Sci, Beijing, Peoples R China |
| 推荐引用方式 GB/T 7714 | Sun, Xiaoming,Sun, Yuan,Wu, Kewen,et al. On the relationship between energy complexity and other boolean function measures[J]. JOURNAL OF COMBINATORIAL OPTIMIZATION,2021:23. |
| APA | Sun, Xiaoming,Sun, Yuan,Wu, Kewen,&Xia, Zhiyu.(2021).On the relationship between energy complexity and other boolean function measures.JOURNAL OF COMBINATORIAL OPTIMIZATION,23. |
| MLA | Sun, Xiaoming,et al."On the relationship between energy complexity and other boolean function measures".JOURNAL OF COMBINATORIAL OPTIMIZATION (2021):23. |
入库方式： OAI收割
来源：计算技术研究所
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