Full Text:   <2077>

Summary:  <1422>

CLC number: TN431

On-line Access: 2017-12-04

Received: 2016-03-05

Revision Accepted: 2016-08-14

Crosschecked: 2017-11-03

Cited: 0

Clicked: 5772

Citations:  Bibtex RefMan EndNote GB/T7714


Ji-zhong SHEN


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Frontiers of Information Technology & Electronic Engineering  2017 Vol.18 No.10 P.1644-1653


An algorithm for identifying symmetric variables based on the order eigenvalue matrix

Author(s):  Xiao-hua Li, Ji-zhong Shen

Affiliation(s):  Campus Information Center, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   jzshen@zju.edu.cn

Key Words:  Boolean function, Symmetric variable, Boolean logic algebra system, Order eigenvalue matrix, Truth table

Xiao-hua Li, Ji-zhong Shen. An algorithm for identifying symmetric variables based on the order eigenvalue matrix[J]. Frontiers of Information Technology & Electronic Engineering, 2017, 18(10): 1644-1653.

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T1 - An algorithm for identifying symmetric variables based on the order eigenvalue matrix
A1 - Xiao-hua Li
A1 - Ji-zhong Shen
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 18
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SP - 1644
EP - 1653
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/FITEE.1601052

To simplify the process for identifying 12 types of symmetric variables in boolean functions, we propose a new symmetry detection algorithm based on minterm expansion or the truth table. First, the order eigenvalue matrix based on a truth table is defined according to the symmetry definition of a logic variable. By analyzing the constraint conditions of the order eigenvalue matrix for 12 types of symmetric variables, an algorithm is proposed for identifying symmetric variables of the boolean function. This algorithm can be applied to identify the symmetric variables of boolean functions with or without don’t-care terms. The proposed method avoids the restriction by the number of logic variables of the graphical method, spectral coefficient methods, and AND-XOR expansion coefficient methods, and solves the problem of completeness in the fast computation method. The algorithm has been implemented in C language and tested on MCNC91 benchmarks. The application results show that, compared with the traditional methods, the new algorithm is an optimal detection method in terms of the applicability of the number of logic variables, the boolean function including don’t-care terms, detection type, and complexity of the identification process.




Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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