論文 Conservation Rules of Direct Sum Decomposition of Groups Formalized Mathematics,24(1):81-94 2016 Author:Kazuhisa Nakasho, Hiroshi Yamazaki, Hiroyuki Okazaki, Yasunari Shidama
Algebra of Polynomially Bounded Sequences and Negligible Functions Formalized Mathematics,23(4):371-378 2016 Author:Hiroyuki Okazaki
Torsion Part of ℤ-module Formalized Mathematics,23(4):297-307 2016 Author:Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama
Equivalent Expressions of Direct Sum Decomposition of Groups Formalized Mathematics,23(1):67-73 2015 Author:Kazuhisa Nakasho, Hiroyuki Okazaki, Hiroshi Yamazaki, Yasunari Shidama
Definition and Properties of Direct Sum Decomposition of Groups Formalized Mathematics,23(1):15-27 2015 Author:Kazuhisa Nakasho, Hiroshi Yamazaki, Hiroyuki Okazaki, Yasunari Shidama
Difference of Function on Vector Space over F Formalized Mathematics,22(3):265-270 2014 Author:Kenichi Arai, Ken Wakabayashi, Hiroyuki Okazaki
Rank of Submodule, Linear Transformations and Linearly Independent Subsets of Z-module Formalized Mathematics,22(3):189-198 2014 Author:Kazuhisa Nakasho, Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama
Formal definition of probability on finite and discrete sample space for proving security of cryptographic systems using Mizar Artificial Intelligence Research,2(4):37-48 2013(Aug.) Author:Okazaki, H; Futa, Y; Shidama, Y
Formalization of Definitions and Theorems Related to an Elliptic Curve Over a Finite Prime Field by Using Mizar JOURNAL OF AUTOMATED REASONING,50(2):161-172 2013(Feb.) Author:Futa, Y; Okazaki, H; Shidama, Y
Isomorphisms of Direct Products of Cyclic Groups of Prime-power Order Formalized Mathematics,21(3):207-211 2013 Author:Hiroshi Yamazaki, Hiroyuki Okazaki, Kazuhisa Nakasho, Yasunari Shidama
Isomorphisms of Direct Products of Finite Commutative Groups Formalized Mathematics,21(1):65-74 2013 Author:Hiroyuki Okazaki, Hiroshi Yamazaki, Yasunari Shidama
Random Variables and Product of Probability Spaces Formalized Mathematics,21(1):33-39 2013 Author:Hiroyuki Okazaki, Yasunari Shidama
The C^k Space Formalized Mathematics,21(1):25-31 2013 Author:Katuhiko Kanazashi, Hiroyuki Okazaki, Yasunari Shidama
Isomorphisms of Direct Products of Finite Cyclic Groups Formalized Mathematics,20(4):343-347 2012 Author:Kenichi Arai, Hiroyuki Okazaki, Yasunari Shidama
Posterior Probability on Finite Set Formalized Mathematics,20(4):257-263 2012 Author:Hiroyuki Okazaki
Operations of Points on Elliptic Curve in Projective Coordinates Formalized Mathematics,20(1):87-95 2012 Author:Yuichi Futa, Hiroyuki Okazaki, Daichi Mizushima, Yasunari Shidama
Set of Points on Elliptic Curve in Projective Coordinates Formalized Mathematics,19(3):131-138 2011 Author:Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama
Banach Algebra of Bounded Complex-Valued Functionals Formalized Mathematics,19(2):121-126 2011 Author:Katuhiko Kanazashi, Hiroyuki Okazaki and Yasunari Shidama
Differentiable Functions into Real Normed Spaces Formalized Mathematics,19(2):69-72 2011 Author:Hiroyuki Okazaki, Noboru Endou, Keiko Narita and Yasunari Shidama
Formalization of Integral Linear Space Formalized Mathematics,19(1):61-64 2011 Author:Hiroyuki Okazaki, Noboru Endou and Yasunari Shidama
Cartesian Products of Family of Real Linear Spaces Formalized Mathematics,19(1):51-59 2011 Author:Hiroyuki Okazaki, Noboru Endou and Yasunari Shidama
More on Continuous Functions on Normed Linear Spaces Formalized Mathematics,19(1):45-49 2011 Author:Hiroyuki Okazaki, Noboru Endou and Yasunari Shidama
Normal Subgroup of Product of Groups Formalized Mathematics,19(1):23-26 2011 Author:Hiroyuki Okazaki, Kenichi Arai, Yasunari Shidama
Probability Measure on Discrete Spaces and Algebra of Real Valued Random Variables Formalized Mathematics,18(4):213-217 2010 Author:Hiroyuki Okazaki, Yasunari Shidama
Properties of Primes and Multiplicative Group of a Field Formalized Mathematics,17(2):151-155 2009 Author:Kenichi Arai,Hiroyuki Okazaki
Probability on Finite Set and Real-Valued Random Variables Formalized Mathematics,17(2):129-136 2009 Author:Hiroyuki Okazaki,Yasunari Shidama
Probability on Finite and Discrete Set and Uniform Distribution Formalized Mathematics,17(2):173-178 2009 Author:Hiroyuki Okazaki
Uniqueness of Factoring an Integer and Multiplicative Group Z/pZ* Formalized Mathematics,16(2):103-107 2008 Author:Hiroyuki Okazaki,Yasunari Shidama
Preliminary Study on a Watermarking Scheme Using Background Pattern to Protect Printed Documents Journal of Signal Processing,11(4):337-340 2007 Author:Katsuki Kobayashi,Heman Aguirre,Hiroyuki Okazaki,Kiyoshi Tanaka
Inferior Limit, Superior Limit and Convergence of Sequences of Extended Real Numbers Formalized Mathematics,15(4):231-235 2007 Author:Hiroshi Yamazaki, Noboru Endou, Yasunari Shidama,Hiroyuki Okazaki
Formalization of Statistical Indistinguishability of Probability Distribution Ensembles in Mizar IEICE , The International Symposium on Information Theory and Its Applications , :517-521 2016 Author:Hiroyuki Okazaki
Privacy Preserving Logic Formula Calculation in Cloud IEEE , 2016 IEEE Tenth International Conference on Semantic Computing (ICSC) , :329-332 2016 Author:Hiroshi Yamaguchi, Shigeo Tsujii, Hiroyuki Okazaki, Yasunari Shidama
Formalization of Binary Fields and N-dimensional Binary Vector Spaces Using the Mizar Proof Checker World Congress in Computer Science, Computer Engineering, and Applied Computing , 2013 International Conference on Foundations of Computer Science (FCS'13) , :71-77 2013 Author:Kenichi Arai, Hiroyuki Okazaki, Yasunari Shidama
Formalization Description of Huffman Coding Trees Using the Mizar World Congress in Computer Science, Computer Engineering, and Applied Computing , 2013 International Conference on Foundations of Computer Science (FCS'13) , :59-65 2013 Author:Takaya Ido, Hiroyuki Okazaki, Yasunari Shidama
Content Development for Distance Education in Advanced University Mathematics Using Mizar World Congress in Computer Science, Computer Engineering, and Applied Computing , The 2013 International Conference on e-Learning, e-Business, Enterprise Information Systems, and e-Government(EEE'13) , :312-326 2013 Author:Takaya Ido, Hiroyuki Okazaki, Hiroshi YAMAZAKI, Pauline Naomi KAWAMOTO, Katsumi WASAKI, Yasunari Shidama
Signature as Public Key Structured Cryptosystem and its Application World Congress in Computer Science, Computer Engineering, and Applied Computing , The 11th International Conference on Security and Management(SAM'12) , :22-27 2012 Author:Kenichi Arai, Hiroyuki Okazaki
Formalization Verification of Number Theoretic Algorithms Using the Mizar Proof Checker World Congress in Computer Science, Computer Engineering, and Applied Computing , 2012 International Conference on Foundations of Computer Science (FCS'12) , :45-50 2012 Author:Hiroyuki Okazaki, Yoshiki Aoki, Yasunari Shidama
Formalization Verification of AES Using the Mizar Proof Checker World Congress in Computer Science, Computer Engineering, and Applied Computing , 2012 International Conference on Foundations of Computer Science (FCS'12) , :78-84 2012 Author:Hiroyuki Okazaki, Kenichi Arai, Yasunari Shidama
Formalization of Gaussian Integers, Gaussian Rational Numbers, and Their Algebraic Structures with Mizar IEICE , 2012 International Symposium on Information Theory and its Applications (ISITA2012) , :591-595 2012 Author:Yuichi Futa, Daichi Mizushima,Hiroyuki Okazaki
Formalization Verification of DES Using the Mizar Proof Checker World Congress in Computer Science, Computer Engineering, and Applied Computing , 2011 International Conference on Foundations of Computer Science , :63-68 2011(Jul.) Author:Hiroyuki Okazaki, Kenichi Arai, Yasunari Shidama
Formalization of Probability and Random Sampling on a Finite and Discrete Sample Space Using the Mizar Proof Checker World Congress in Computer Science, Computer Engineering, and Applied Computing , 2010 International Conference on Foundations of Computer Science 2010(Jul.) Author:Kenichi Arai, Nobuaki Kondo, Hiroyuki Okazaki
An evolutionary multiobjective approach to design highly non-linear Boolean functions ACM , Genetic and Evolutionary Computation Conference (GECCO 2007) , :749-756 2007 Author:Hernan E. Aguirre, Hiroyuki Okazaki, Yasushi Fuwa
A watermarking scheme using background pattern to protect printed documents 信号処理学会 , Proc. International Workshop on Nonlinear Circuits and Signal Processing (NCSP 2007) 2007 Author:Katsuki Kobayashi, Kiyoshi Tanaka, Hernan Aguirre, Hiroyuki Okazaki, Hisayoshi Kunimune,Katsumi Wasaki, Masaaki Niimura, Yasushi Fuwa
その他 Formalization of Polynomially Bounded and Negligible Functions Using the Computer-Aided Proof-Checking System Mizar CEUR Workshop Proceedings , International Conference on Information and Knowledge Management (CIKM) FM4M/MathUI/ThEdu/DP/WIP@CIKM 2016 , :117-131 2016 Author:Hiroyuki Okazaki, Yuichi Futa
Formal Definition of Probability and Probabilistic Function on Finite and Discrete Sample Space for Proving Security of Cryptographic Systems Using Mizar. American Mathematical Society (AMS) and the Mathematical Association of America (MAA) , 2011 Joint Mathematics Meetings (JMM2011) , (1067-94-740):156 2011(Jan. 09) Author:Hiroyuki Okazaki, Yasunari Shidama,Yuichi Futa
Meta Ring Signature Scheme IACR , Cryptology ePrint Archive , (2005/310) 2005 Author:H. Okazaki, R. Sakai and M.Kasahara
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