A New Pairwise NPN Boolean Matching Algorithm Based on Structural Difference Signature

Zhang, Juling; Yang, Guowu; Hung, William N. N.; Wu, Jinzhao; Zhu, Yixin

doi:10.3390/sym11010027

Cited by 3 publications

(3 citation statements)

References 23 publications

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“…They addressed a pairwise matching algorithm based on the 1 st and 2 nd general signatures. A fast pairwise Boolean matching algorithm was proposed in Reference [18], which made full use of the cofactor signature, Boolean difference signature and symmetric variables. References [19] and [20] both used signatures to reduce the complexity of pairwise comparisons.…”

Section: Related Workmentioning

confidence: 99%

“…Definition 7 (Independent Variable): Variable x i of Boolean function f is an independent variable when |f x i | = 0, where [18].…”

Section: Preliminaries a Boolean Function And Npn Equivalentmentioning

confidence: 99%

“…Therefore, the key issue of the canonical-based Boolean matching algorithm is finding the canonical form [9], [10], [11], [12], [13], [14], [15], [16]. Pairwise comparison algorithms utilise signature differentiated variables and search the variable correspondence relation between two Boolean functions [1], [17], [18], [19], [20]. Therefore, the most important consideration is the choice and use of signatures.…”

Section: Introductionmentioning

confidence: 99%

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A Heuristic Boolean NPN Equivalent Matching Verification Method Based on Shannon Decomposition

et al. 2022

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In this paper, we describe a new verification method to accelerate the input negation and/or input permutation and/or output negation (NPN) Boolean matching for a single-output completely specified Boolean function. Through research on the Boolean Shannon decomposition binary tree, we prove that the signature vectors of the left child node and right child node are complementary relative to the signature vector of the parent node. We introduce an independent variable check to speed up the detection of candidate transformation. The proposed approach utilises this complementarity, a symmetry check, an independent variable check and a phase collision check, which can quickly verify whether the candidate transformation obtained in the detection of the candidate transformation of the Boolean matching process is accurate. We perform experiments on two types of Boolean function sets. One type consists of Boolean functions from randomly generated circuits. The other is exported from the Microelectronics Center of North Carolina (MCNC) benchmark. The experimental results show that the average runtime of our algorithm is 68.8% faster than those in on two randomly generated circuits and 51% faster than those in when tested on the MCNC benchmark circuit set. Therefore, the experimental results demonstrate the effectiveness of the proposed method.INDEX TERMS Boolean matching, NPN equivalence, Shannon expansion, Shannon decomposition binary tree, signature vector.

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Section: Related Workmentioning

confidence: 99%

“…Definition 7 (Independent Variable): Variable x i of Boolean function f is an independent variable when |f x i | = 0, where [18].…”

Section: Preliminaries a Boolean Function And Npn Equivalentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Heuristic Boolean NPN Equivalent Matching Verification Method Based on Shannon Decomposition

et al. 2022

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Hamacher heronian mean operators for multi-critria decision-making under multi-valued picture fuzzy uncertain lingsuitic environment

Yang

2021

IFS

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Picture fuzzy set (PFS) and linguistic term set (LTS) are two significant notions in multi-criteria decision-making (MCDM). In practice, decision-makers sometimes need utilize the multiple probable membership degrees for an uncertain linguistic term to express evaluation information. Motivated by these, to better convey the vagueness and uncertainty of cognitive information, multi-valued picture fuzzy uncertain linguistic set combining picture hesitant fuzzy set with uncertain linguistic term set is proposed. We firstly define the concepts of multi-valued picture fuzzy uncertain linguistic set and multi-valued picture fuzzy uncertain linguistic number. Hamacher operations are more general and flexible in information fusion, thus, Hamacher operations and comparison method are developed at the same time. Improved generalized Heronian Mean operator can simultaneously reflect correlations between values and prevent the redundant calculation. Then, two operators of improved generalized weighted Heronian mean and improved generalized geometric weighted Heronian mean in view of Hamacher operations are proposed. Meanwhile, some distinguished properties and instances of two operators are explored as well. Moreover, a novel MCDM approach applying the developed operators is constructed. Ultimately, an illustrative example on vendor selection is performed, and sensitivity analysis and comparison analysis are provided to verify the powerfulness of the proposed method.

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A new multi-criteria decision-making method utilizing power heronian operators with picture hesitant fuzzy information

Yang

Qian

2022

IFS

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In practice, picture hesitant fuzzy sets (PHFSs) combining the picture fuzzy sets (PFSs) and hesitant fuzzy sets (HFSs) are suitable to represent more complex multi-criteria decision-making (MCDM) information. The power heronian (PH) operators, which have the merits of power average (PA) and heronian mean (HM) operators, are extended to the environment of PHFSs in this article. First, some algebraic operations of picture hesitant fuzzy numbers (PHFNs), comparative functions and distance measure are introduced. Second, two novel operators, called as picture hesitant fuzzy weighted power heronian (PHFWPH) operator and picture hesitant fuzzy weighted geometric power heronian (PHFWGPH) operator, are defined. Meanwhile, some desirable characteristics and special instances of two operators are investigated as well. Third, a novel MCDM approach applying the proposed PH operators to handle PHFNs is explored. Lastly, to indicate the effectiveness of this novel method, an example regarding MCDM problem is conducted, as well as sensitivity and comparison analysis.

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A New Pairwise NPN Boolean Matching Algorithm Based on Structural Difference Signature

Cited by 3 publications

References 23 publications

A Heuristic Boolean NPN Equivalent Matching Verification Method Based on Shannon Decomposition

A Heuristic Boolean NPN Equivalent Matching Verification Method Based on Shannon Decomposition

Hamacher heronian mean operators for multi-critria decision-making under multi-valued picture fuzzy uncertain lingsuitic environment

A new multi-criteria decision-making method utilizing power heronian operators with picture hesitant fuzzy information

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