Reed-Muller logic is becoming increasingly attractive. However, its synthesis and optimization are difficult especially for mixed polarity Reed-Muller logic. In this paper, a function is expressed into a truth vector....Reed-Muller logic is becoming increasingly attractive. However, its synthesis and optimization are difficult especially for mixed polarity Reed-Muller logic. In this paper, a function is expressed into a truth vector. Product shrinkage, general sum shrinkage （GSS）, elimination and extraction operators are proposed to shrink the truth vector. A novel algorithm is presented to derive a compact Multi-level Mixed Polarity Reed-Muller Form （MMPRMF） starting from a given fixed polarity truth vector. The results show that a significant area improvement can be made compared with published results.展开更多
By mapping a fixed polarity Reed-Muller (RM) expression into an onset table and studying the properties of the onset table,an algorithm is proposed to obtain a compact multi-level single-output mixed-polarity RM funct...By mapping a fixed polarity Reed-Muller (RM) expression into an onset table and studying the properties of the onset table,an algorithm is proposed to obtain a compact multi-level single-output mixed-polarity RM function by searching for and extracting the common variables using the onset table.Furthermore,by employing the multiplexer model,the algorithm is extended to optimize multi-level multi-output mixed-polarity RM forms.The proposed algorithm is implemented in C language and tested using some MCNC benchmarks.Experimental results show that the proposed algorithm can obtain a more compact RM form than that under fixed polarity.Compared with published results,the proposed algorithm makes a significant speed improvement,with a small increase in the number of literals.展开更多
Conversion of the Reed–Muller（RM） expansion between two different polarities is an important step in the synthesis and optimization of RM circuits. By investigating XOR decomposition, a new conversion algorithm is ...Conversion of the Reed–Muller（RM） expansion between two different polarities is an important step in the synthesis and optimization of RM circuits. By investigating XOR decomposition, a new conversion algorithm is proposed to convert MPRM expansion from one polarity to another. First, the relationship between XOR decomposition and mixed polarity is set up. Second, based on this, the operation relation of term coefficients between the two polarities is derived to realize MPRM expansion conversion. And finally, with the MCNC Benchmark, the resultsofouralgorithmshowthatitismoresuitablefordealingwithMPRMexpansionwithmoreterms.Compared to the previous tabular technique, the conversion efficiency is improved up to approximately 44.39%.展开更多
In this paper,we first introduce a concept of L_p-dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar projection Aleksandrov-Fenchel inequality for...In this paper,we first introduce a concept of L_p-dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar projection Aleksandrov-Fenchel inequality for L_p-dual Quermassintegral sums.Moreover,by using Lutwak’s width-integral of index i,we establish the L_p-Brunn-Minkowski inequality for the polar mixed projec- tion bodies.As applications,we prove some interrelated results.展开更多
文摘Reed-Muller logic is becoming increasingly attractive. However, its synthesis and optimization are difficult especially for mixed polarity Reed-Muller logic. In this paper, a function is expressed into a truth vector. Product shrinkage, general sum shrinkage （GSS）, elimination and extraction operators are proposed to shrink the truth vector. A novel algorithm is presented to derive a compact Multi-level Mixed Polarity Reed-Muller Form （MMPRMF） starting from a given fixed polarity truth vector. The results show that a significant area improvement can be made compared with published results.
基金Project supported by the National Natural Science Foundation of China (Nos.60871022 and 61041001)the Natural Science Foundation of Zhejiang Province (Nos.Z1090622 and Y1080654)the Ningbo Natural Science Foundation,China (No.2010A610183)
文摘By mapping a fixed polarity Reed-Muller (RM) expression into an onset table and studying the properties of the onset table,an algorithm is proposed to obtain a compact multi-level single-output mixed-polarity RM function by searching for and extracting the common variables using the onset table.Furthermore,by employing the multiplexer model,the algorithm is extended to optimize multi-level multi-output mixed-polarity RM forms.The proposed algorithm is implemented in C language and tested using some MCNC benchmarks.Experimental results show that the proposed algorithm can obtain a more compact RM form than that under fixed polarity.Compared with published results,the proposed algorithm makes a significant speed improvement,with a small increase in the number of literals.
基金Project supported by the National Natural Science Foundation of China(Nos.61076032,61234002)the Natural Science Foundation of Zhejiang Province(Nos.Z1111219,LY12D06002,LY13F040003)K.C.Wong Magna Fund in Ningbo University
文摘Conversion of the Reed–Muller（RM） expansion between two different polarities is an important step in the synthesis and optimization of RM circuits. By investigating XOR decomposition, a new conversion algorithm is proposed to convert MPRM expansion from one polarity to another. First, the relationship between XOR decomposition and mixed polarity is set up. Second, based on this, the operation relation of term coefficients between the two polarities is derived to realize MPRM expansion conversion. And finally, with the MCNC Benchmark, the resultsofouralgorithmshowthatitismoresuitablefordealingwithMPRMexpansionwithmoreterms.Compared to the previous tabular technique, the conversion efficiency is improved up to approximately 44.39%.
基金This work was partially supported by the National Natural Science Foundation of China (Grant No.10271071)Zhejiang Provincial Natural Science Foundation of China (Grant No.Y605065)Foundation of the Education Department of Zhejiang Province of China (Grant No.20050392)
文摘In this paper,we first introduce a concept of L_p-dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar projection Aleksandrov-Fenchel inequality for L_p-dual Quermassintegral sums.Moreover,by using Lutwak’s width-integral of index i,we establish the L_p-Brunn-Minkowski inequality for the polar mixed projec- tion bodies.As applications,we prove some interrelated results.
