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Formalization Of Matrix Theory In Hol4, Zhiping Shi, Yan Zhang, Zhenke Liu, Xinan Kang, Yong Guan, Jie Zhang, Xiaoyu Song
Formalization Of Matrix Theory In Hol4, Zhiping Shi, Yan Zhang, Zhenke Liu, Xinan Kang, Yong Guan, Jie Zhang, Xiaoyu Song
Yong Guan
Matrix theory plays an important role in modeling linear systems in engineering and science. To model and analyze the intricate behavior of complex systems, it is imperative to formalize matrix theory in a metalogic setting. This paper presents the higherorder logic (HOL) formalization of the vector space and matrix theory in the HOL4 theorem proving system. Formalized theories include formal definitions of real vectors and matrices, algebraic properties, and determinants, which are verified in HOL4. Two case studies, modeling and verifying composite two-port networks and state transfer equations, are presented to demonstrate the applicability and effectiveness of our work.
Formalization Of Matrix Theory In Hol4, Zhiping Shi, Yan Zhang, Zhenke Liu, Xinan Kang, Yong Guan, Jie Zhang, Xiaoyu Song
Formalization Of Matrix Theory In Hol4, Zhiping Shi, Yan Zhang, Zhenke Liu, Xinan Kang, Yong Guan, Jie Zhang, Xiaoyu Song
Electrical and Computer Engineering Faculty Publications and Presentations
Matrix theory plays an important role in modeling linear systems in engineering and science. To model and analyze the intricate behavior of complex systems, it is imperative to formalize matrix theory in a metalogic setting. This paper presents the higherorder logic (HOL) formalization of the vector space and matrix theory in the HOL4 theorem proving system. Formalized theories include formal definitions of real vectors and matrices, algebraic properties, and determinants, which are verified in HOL4. Two case studies, modeling and verifying composite two-port networks and state transfer equations, are presented to demonstrate the applicability and effectiveness of our work.
Technology Corner: Calculating The Number Of Android Lock Patterns: An Unfinished Study In Number Theory, Gary C. Kessler
Technology Corner: Calculating The Number Of Android Lock Patterns: An Unfinished Study In Number Theory, Gary C. Kessler
Security Studies & International Affairs - Daytona Beach
"Although one is unlikely to ever want to brute-force an Android lock pattern, many do wonder about the relative strength of the lock pattern versus a multi-digit personal identification number (PIN). It becomes obvious pretty quickly that there are many more lock patterns than the 10,000 possible four-digit PINs."--from the introduction.