Solving logic equation via matrix expression

Frontiers of Electrical and Electronic Engineering in China

Volumn 4, Issue 3, 2009, Pages 259-269

  Cheng, Daizhan ^a   Li, Zhiqiang ^a  

^a INSTITUTE OF SYSTEMS SCIENCE   (China)

Author keywords

Logic equation; Logic inference; Semi tensor product; Structure matrix

Indexed keywords

EID: 70349808245     PISSN: 16733460     EISSN: 16733584     Source Type: Journal    
DOI: 10.1007/s11460-009-0040-z     Document Type: Article

References (18)

1. Zhao Q, Zheng D, Zhu X. Structure properties of min-max systems and existence of global cycle time. IEEE Transactions on Automatic Control, 2001, 41(1): 148-151.
2. Verbruggen H B, Babuska R. Fuzzy Logic Control in Applications. Singapore: World Scientific, 1999.
3. Wu S F, Engelen C J H, Babuska R, Chu Q P, Mulder J A. Intelligent flight controller design with fuzzy logic for an atmospheric re-entry vehicle. In: Proceedings of the 38th Aerospace Sciences Meeting and Exhibit, Reno, NV. 2000, AIAA-2000-174.
4. Claudio D P, Raffaella D S, Morse A S. Supervisory control with state-dependent dwell-time logic and constraints. Automatica, 2004, 40(2): 269-275.
5. Ideker T, Galitski T, Hood L. A new approach to decoding life: systems biology. Annual Review of Genomics and Human Genetics, 2001, 2: 343-372.
6. Kitano H. Systems biology: a brief overview. Science, 2002, 259 (5560): 1662-1664.
7. Kauffman S A. Metabolic stability and epigenesist in randomly constructed genetic nets. Journal Theoretical Biology, 1969, 22(3): 437-467.
8. Farrow C, Heidel J, Maloney H, Rogers J. Scalar equations for synchronous Boolean networks with biological applications. IEEE Transactions on Neural Networks, 2004, 15(2): 348-354.
9. Cheng D, Qi H. A linear representation of dynamics of Boolean networks. IEEE Transactions on Automatic Control (accepted).
10. Cheng D. Input-state approach to Boolean control networks. IEEE Transactions on Neural Networks, 2009, 20(3): 512-521.
11. Cheng D, Qi H. Controllability and observability of Boolean control networks. Automatica (to appear).
12. Cheng D, Qi H. Semi-tensor Product of Matrices-Theory and Applications. Beijing: Science Press, 2007 (in Chinese).
13. Cheng D. Semi-tensor product of matrices and its applications-a survey. In: Proceedings of the 6th ICCM'07, Hangzhou. 2007, 3: 641-668.
14. Magnus J R, Neudecker H. Matrix Differential Calculus with Applications in Statistics and Econometrics. 2nd ed. New York: John Wiley & Sons, 1999.
15. Cheng D. On logic-based intelligent systems. In: Proceedings of ICCA 2005, Budapest. 2005, 71-76.
16. Cheng D, Qi H. Matrix expression of logic and fuzzy control. In: Proceedings of the 44th IEEE CDC, Seville. 2005, 3273-3278.
17. Barnes D W. An Algebraic Introduction to Mathematical Logic. New York: Springer-Verlag, 1975.
18. Rade L, Westergren B. Mathematics Handbook for Science and Engineering. 4th ed. Lund: Studentlitteratur, 1998.