? A Power and Area Optimization Approach of Mixed Polarity Reed-Muller Expression for Incompletely Specified Boolean Functions
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Journal of Computer Science and Technology 2017, Vol. 32 Issue (2) :297-311    DOI: 10.1007/s11390-017-1723-1
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A Power and Area Optimization Approach of Mixed Polarity Reed-Muller Expression for Incompletely Specified Boolean Functions
Zhen-Xue He1,2, Li-Min Xiao1,2,*, Senior Member, CCF, Li Ruan1,2, Senior Member, CCF, Fei Gu2, Zhi-Sheng Huo1,2, Guang-Jun Qin3, Member, CCF, Ming-Fa Zhu1,2, Senior Member, CCF, Long-Bing Zhang4,5, Rui Liu3,6, Xiang Wang3
1 State Key Laboratory of Software Development Environment, Beihang University, Beijing 100191, China;
2 School of Computer Science and Engineering, Beihang University, Beijing 100191, China;
3 School of Electronic and Information Engineering, Beihang University, Beijing 100191, China;
4 State Key Laboratory of Computer Architecture, Institute of Computing Technology, Chinese Academy of Sciences Beijing 100190, China;
5 University of Chinese Academy of Sciences, Beijing 100049, China;
6 National Engineering Research Center for Science and Technology Resources Sharing Service, Beihang University Beijing 100191, China

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Abstract The power and area optimization of Reed-Muller (RM) circuits has been widely concerned. However, almost none of the exiting power and area optimization approaches can obtain all the Pareto optimal solutions of the original problem and are efficient enough. Moreover, they have not considered the don't care terms, which makes the circuit performance unable to be further optimized. In this paper, we propose a power and area optimization approach of mixed polarity RM expression (MPRM) for incompletely specified Boolean functions based on Non-Dominated Sorting Genetic Algorithm II (NSGA-II). Firstly, the incompletely specified Boolean function is transformed into zero polarity incompletely specified MPRM (ISMPRM) by using a novel ISMPRM acquisition algorithm. Secondly, the polarity and allocation of don't care terms of ISMPRM is encoded as chromosome. Lastly, the Pareto optimal solutions are obtained by using NSGA-II, in which MPRM corresponding to the given chromosome is obtained by using a chromosome conversion algorithm. The results on incompletely specified Boolean functions and MCNC benchmark circuits show that a significant power and area improvement can be made compared with the existing power and area optimization approaches of RM circuits.
Articles by authors
Zhen-Xue He
Li-Min Xiao
Li Ruan
Fei Gu
Zhi-Sheng Huo
Guang-Jun Qin
Ming-Fa Zhu
Long-Bing Zhang
Rui Liu
Xiang Wang
Keywordspower and area optimization   Reed-Muller (RM) circuit   Pareto optimal solution   don't care term   chromosome conversion     
Received 2015-12-19;
Fund:

This work is supported by the National Natural Science Foundation of China under Grant Nos. 60973106, 61370059, 61232009, and 81571142, Beijing Natural Science Foundation under Grant No. 4152030, the Fundamental Research Funds for the Central Universities of China under Grant Nos. YWF-15-GJSYS-085 and YWF-14-JSJXY-14, the Fund of the State Key Laboratory of Computer Architecture of China under Grant No. CARCH201507, the Open Project Program of National Engineering Research Center for Science and Technology Resources Sharing Service (Beihang University), and the Fund of the State Key Laboratory of Software Development Environment of China under Grant No. SKLSDE-2016ZX-15.

Corresponding Authors: Li-Min Xiao     Email: xiaolm@buaa.edu.cn
About author: Zhen-Xue He is a Ph.D. candidate in the School of Computer Science and Engineering, Beihang University, Beijing. He received his M.S. degree in computer application technology from Northwest Normal University, Lanzhou, in 2014. His research interests include electronic design automation, low power design and artificial intelligence.
Cite this article:   
Zhen-Xue He, Li-Min Xiao, Li Ruan, Fei Gu, Zhi-Sheng Huo, Guang-Jun Qin, Ming-Fa Zhu, Long-Bing Zhang, Rui Liu, Xiang Wang.A Power and Area Optimization Approach of Mixed Polarity Reed-Muller Expression for Incompletely Specified Boolean Functions[J]  Journal of Computer Science and Technology, 2017,V32(2): 297-311
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