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A Power and Area Optimization Approach of Mixed Polarity Reed-Muller Expression for Incompletely Specified Boolean Functions

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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.

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Authors and Affiliations

  1. State Key Laboratory of Software Development Environment, Beihang University, Beijing, 100191, China

    Zhen-Xue He, Li-Min Xiao, Li Ruan, Zhi-Sheng Huo & Ming-Fa Zhu

  2. School of Computer Science and Engineering, Beihang University, Beijing, 100191, China

    Zhen-Xue He, Li-Min Xiao, Li Ruan, Fei Gu, Zhi-Sheng Huo & Ming-Fa Zhu

  3. School of Electronic and Information Engineering, Beihang University, Beijing, 100191, China

    Guang-Jun Qin, Rui Liu & Xiang Wang

  4. State Key Laboratory of Computer Architecture, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, 100190, China

    Long-Bing Zhang

  5. University of Chinese Academy of Sciences, Beijing, 100049, China

    Long-Bing Zhang

  6. National Engineering Research Center for Science and Technology Resources Sharing Service, Beihang University, Beijing, 100191, China

    Rui Liu

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  1. Zhen-Xue He
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  2. Li-Min Xiao
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  3. Li Ruan
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  10. Xiang Wang
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Correspondence to Li-Min Xiao.

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He, ZX., Xiao, LM., Ruan, L. et al. A Power and Area Optimization Approach of Mixed Polarity Reed-Muller Expression for Incompletely Specified Boolean Functions. J. Comput. Sci. Technol. 32, 297–311 (2017). https://doi.org/10.1007/s11390-017-1723-1

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  • DOI: https://doi.org/10.1007/s11390-017-1723-1

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