BibTeX records: Hiroyuki Okazaki

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@article{DBLP:journals/fm/Okazaki23,
  author       = {Hiroyuki Okazaki},
  title        = {On the Formalization of Gram-Schmidt Process for Orthonormalizing
                  a Set of Vectors},
  journal      = {Formaliz. Math.},
  volume       = {31},
  number       = {1},
  pages        = {53--57},
  year         = {2023},
  url          = {https://doi.org/10.2478/forma-2023-0005},
  doi          = {10.2478/FORMA-2023-0005},
  timestamp    = {Wed, 04 Oct 2023 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/Okazaki23.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/Okazaki22,
  author       = {Hiroyuki Okazaki},
  title        = {Formalization of Orthogonal Decomposition for Hilbert Spaces},
  journal      = {Formaliz. Math.},
  volume       = {30},
  number       = {4},
  pages        = {295--299},
  year         = {2022},
  url          = {https://doi.org/10.2478/forma-2022-0023},
  doi          = {10.2478/FORMA-2022-0023},
  timestamp    = {Wed, 01 Mar 2023 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/Okazaki22.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/NakashoOS21,
  author       = {Kazuhisa Nakasho and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Real Vector Space and Related NotionsThis study was supported in part
                  by {JSPS} {KAKENHI} Grant Numbers 17K00182 and 20K19863},
  journal      = {Formaliz. Math.},
  volume       = {29},
  number       = {3},
  pages        = {117--127},
  year         = {2021},
  url          = {https://doi.org/10.2478/forma-2021-0012},
  doi          = {10.2478/FORMA-2021-0012},
  timestamp    = {Fri, 21 Jan 2022 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/NakashoOS21.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/NakashoOS21a,
  author       = {Kazuhisa Nakasho and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Finite Dimensional Real Normed Spaces are Proper Metric Spaces},
  journal      = {Formaliz. Math.},
  volume       = {29},
  number       = {4},
  pages        = {175--184},
  year         = {2021},
  url          = {https://doi.org/10.2478/forma-2021-0017},
  doi          = {10.2478/FORMA-2021-0017},
  timestamp    = {Mon, 25 Jul 2022 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/NakashoOS21a.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/OkazakiN21,
  author       = {Hiroyuki Okazaki and
                  Kazuhisa Nakasho},
  title        = {The 3-Fold Product Space of Real Normed Spaces and its Properties},
  journal      = {Formaliz. Math.},
  volume       = {29},
  number       = {4},
  pages        = {241--248},
  year         = {2021},
  url          = {https://doi.org/10.2478/forma-2021-0022},
  doi          = {10.2478/FORMA-2021-0022},
  timestamp    = {Mon, 25 Jul 2022 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/OkazakiN21.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/aina/TokuyamaFSO21,
  author       = {Ryo Tokuyama and
                  Yuichi Futa and
                  Hikofumi Suzuki and
                  Hiroyuki Okazaki},
  editor       = {Leonard Barolli and
                  Isaac Woungang and
                  Tomoya Enokido},
  title        = {Virtual Environment for Analysis and Evaluation of DDoS Attacks},
  booktitle    = {Advanced Information Networking and Applications - Proceedings of
                  the 35th International Conference on Advanced Information Networking
                  and Applications (AINA-2021), Toronto, ON, Canada, 12-14 May, 2021,
                  Volume 3},
  series       = {Lecture Notes in Networks and Systems},
  volume       = {227},
  pages        = {459--468},
  publisher    = {Springer},
  year         = {2021},
  url          = {https://doi.org/10.1007/978-3-030-75078-7\_46},
  doi          = {10.1007/978-3-030-75078-7\_46},
  timestamp    = {Thu, 12 Aug 2021 13:39:25 +0200},
  biburl       = {https://dblp.org/rec/conf/aina/TokuyamaFSO21.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/isita/MienoYOFA20,
  author       = {Takehiko Mieno and
                  Togo Yoshimura and
                  Hiroyuki Okazaki and
                  Yuichi Futa and
                  Kenichi Arai},
  title        = {Formal Verification of Merkle-Damg{\aa}rd Construction in ProVerif},
  booktitle    = {International Symposium on Information Theory and Its Applications,
                  {ISITA} 2020, Kapolei, HI, USA, October 24-27, 2020},
  pages        = {602--606},
  publisher    = {{IEEE}},
  year         = {2020},
  url          = {https://ieeexplore.ieee.org/document/9366163},
  timestamp    = {Mon, 22 Mar 2021 15:48:59 +0100},
  biburl       = {https://dblp.org/rec/conf/isita/MienoYOFA20.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/OkazakiNF19,
  author       = {Hiroyuki Okazaki and
                  Koh{-}ichi Nagao and
                  Yuichi Futa},
  title        = {Maximum Number of Steps Taken by Modular Exponentiation and Euclidean
                  Algorithm},
  journal      = {Formaliz. Math.},
  volume       = {27},
  number       = {1},
  pages        = {87--91},
  year         = {2019},
  url          = {https://doi.org/10.2478/forma-2019-0009},
  doi          = {10.2478/FORMA-2019-0009},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/OkazakiNF19.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/FutaOS19,
  author       = {Yuichi Futa and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Operations of Points on Elliptic Curve in Affine Coordinates},
  journal      = {Formaliz. Math.},
  volume       = {27},
  number       = {3},
  pages        = {315--320},
  year         = {2019},
  url          = {https://doi.org/10.2478/forma-2019-0026},
  doi          = {10.2478/FORMA-2019-0026},
  timestamp    = {Thu, 07 Jan 2021 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/FutaOS19.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/Okazaki18,
  author       = {Hiroyuki Okazaki},
  title        = {Binary Representation of Natural Numbers},
  journal      = {Formaliz. Math.},
  volume       = {26},
  number       = {3},
  pages        = {223--229},
  year         = {2018},
  url          = {https://doi.org/10.2478/forma-2018-0020},
  doi          = {10.2478/FORMA-2018-0020},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/Okazaki18.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/isita/OkazakiFA18,
  author       = {Hiroyuki Okazaki and
                  Yuichi Futa and
                  Kenichi Arai},
  title        = {Suitable Symbolic Models for Cryptographic Verification of Secure
                  Protocols in ProVerif},
  booktitle    = {International Symposium on Information Theory and Its Applications,
                  {ISITA} 2018, Singapore, October 28-31, 2018},
  pages        = {326--330},
  publisher    = {{IEEE}},
  year         = {2018},
  url          = {https://doi.org/10.23919/ISITA.2018.8664273},
  doi          = {10.23919/ISITA.2018.8664273},
  timestamp    = {Wed, 11 Aug 2021 11:51:25 +0200},
  biburl       = {https://dblp.org/rec/conf/isita/OkazakiFA18.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/NakashoYOS16,
  author       = {Kazuhisa Nakasho and
                  Hiroshi Yamazaki and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Conservation Rules of Direct Sum Decomposition of Groups},
  journal      = {Formaliz. Math.},
  volume       = {24},
  number       = {1},
  pages        = {81--94},
  year         = {2016},
  url          = {https://doi.org/10.1515/forma-2016-0007},
  doi          = {10.1515/FORMA-2016-0007},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/NakashoYOS16.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/cikm/OkazakiF16,
  author       = {Hiroyuki Okazaki and
                  Yuichi Futa},
  editor       = {Andrea Kohlhase and
                  Paul Libbrecht and
                  Bruce R. Miller and
                  Adam Naumowicz and
                  Walther Neuper and
                  Pedro Quaresma and
                  Frank Wm. Tompa and
                  Martin Suda},
  title        = {Formalization of Polynomially Bounded and Negligible Functions Using
                  the Computer-Aided Proof-Checking System Mizar},
  booktitle    = {Joint Proceedings of the FM4M, MathUI, and ThEdu Workshops, Doctoral
                  Program, and Work in Progress at the Conference on Intelligent Computer
                  Mathematics 2016 co-located with the 9th Conference on Intelligent
                  Computer Mathematics {(CICM} 2016), Bialystok, Poland, July 25-29,
                  2016},
  series       = {{CEUR} Workshop Proceedings},
  volume       = {1785},
  pages        = {117--131},
  publisher    = {CEUR-WS.org},
  year         = {2016},
  url          = {https://ceur-ws.org/Vol-1785/W38.pdf},
  timestamp    = {Fri, 10 Mar 2023 16:22:32 +0100},
  biburl       = {https://dblp.org/rec/conf/cikm/OkazakiF16.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/isita/Okazaki16,
  author       = {Hiroyuki Okazaki},
  title        = {Formalization of statistical indistinguishability of probability distribution
                  ensembles in Mizar},
  booktitle    = {2016 International Symposium on Information Theory and Its Applications,
                  {ISITA} 2016, Monterey, CA, USA, October 30 - November 2, 2016},
  pages        = {517--521},
  publisher    = {{IEEE}},
  year         = {2016},
  url          = {https://ieeexplore.ieee.org/document/7840478/},
  timestamp    = {Wed, 11 Aug 2021 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/conf/isita/Okazaki16.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/semco/YamaguchiTOS16,
  author       = {Hiroshi Yamaguchi and
                  Shigeo Tsujii and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Privacy Preserving Logic Formula Calculation in Cloud},
  booktitle    = {Tenth {IEEE} International Conference on Semantic Computing, {ICSC}
                  2016, Laguna Hills, CA, USA, February 4-6, 2016},
  pages        = {329--332},
  publisher    = {{IEEE} Computer Society},
  year         = {2016},
  url          = {https://doi.org/10.1109/ICSC.2016.99},
  doi          = {10.1109/ICSC.2016.99},
  timestamp    = {Thu, 23 Mar 2023 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/conf/semco/YamaguchiTOS16.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/NakashoYOS15,
  author       = {Kazuhisa Nakasho and
                  Hiroshi Yamazaki and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Definition and Properties of Direct Sum Decomposition of Groups1},
  journal      = {Formaliz. Math.},
  volume       = {23},
  number       = {1},
  pages        = {15--27},
  year         = {2015},
  url          = {https://doi.org/10.2478/forma-2015-0002},
  doi          = {10.2478/FORMA-2015-0002},
  timestamp    = {Fri, 10 Dec 2021 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/NakashoYOS15.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/FutaOS15,
  author       = {Yuichi Futa and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Matrix of {\(\mathbb{Z}\)}-module1},
  journal      = {Formaliz. Math.},
  volume       = {23},
  number       = {1},
  pages        = {29--49},
  year         = {2015},
  url          = {https://doi.org/10.2478/forma-2015-0003},
  doi          = {10.2478/FORMA-2015-0003},
  timestamp    = {Fri, 10 Dec 2021 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/FutaOS15.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/NakashoOYS15,
  author       = {Kazuhisa Nakasho and
                  Hiroyuki Okazaki and
                  Hiroshi Yamazaki and
                  Yasunari Shidama},
  title        = {Equivalent Expressions of Direct Sum Decomposition of Groups1},
  journal      = {Formaliz. Math.},
  volume       = {23},
  number       = {1},
  pages        = {67--73},
  year         = {2015},
  url          = {https://doi.org/10.2478/forma-2015-0006},
  doi          = {10.2478/FORMA-2015-0006},
  timestamp    = {Fri, 10 Dec 2021 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/NakashoOYS15.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/OkazakiF15,
  author       = {Hiroyuki Okazaki and
                  Yuichi Futa},
  title        = {Polynomially Bounded Sequences and Polynomial Sequences},
  journal      = {Formaliz. Math.},
  volume       = {23},
  number       = {3},
  pages        = {205--213},
  year         = {2015},
  url          = {https://doi.org/10.1515/forma-2015-0017},
  doi          = {10.1515/FORMA-2015-0017},
  timestamp    = {Fri, 10 Dec 2021 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/OkazakiF15.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/FutaOS15a,
  author       = {Yuichi Futa and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Torsion Part of {\(\mathbb{Z}\)}-module},
  journal      = {Formaliz. Math.},
  volume       = {23},
  number       = {4},
  pages        = {297--307},
  year         = {2015},
  url          = {https://doi.org/10.1515/forma-2015-0024},
  doi          = {10.1515/FORMA-2015-0024},
  timestamp    = {Fri, 10 Dec 2021 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/FutaOS15a.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/Okazaki15,
  author       = {Hiroyuki Okazaki},
  title        = {Algebra of Polynomially Bounded Sequences and Negligible Functions},
  journal      = {Formaliz. Math.},
  volume       = {23},
  number       = {4},
  pages        = {371--378},
  year         = {2015},
  url          = {https://doi.org/10.1515/forma-2015-0029},
  doi          = {10.1515/FORMA-2015-0029},
  timestamp    = {Fri, 10 Dec 2021 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/Okazaki15.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/brain/OkazakiMSMM15,
  author       = {Hiroyuki Okazaki and
                  Hiroki Matsumoto and
                  Yoshiki Shibata and
                  Shinichi Motomura and
                  Naoyuki Masada},
  editor       = {Yike Guo and
                  Karl J. Friston and
                  A. Aldo Faisal and
                  Sean L. Hill and
                  Hanchuan Peng},
  title        = {Application to Women's Healthcare of Health Management System Using
                  a Tablet Phone},
  booktitle    = {Brain Informatics and Health - 8th International Conference, {BIH}
                  2015, London, UK, August 30 - September 2, 2015. Proceedings},
  series       = {Lecture Notes in Computer Science},
  volume       = {9250},
  pages        = {262--271},
  publisher    = {Springer},
  year         = {2015},
  url          = {https://doi.org/10.1007/978-3-319-23344-4\_26},
  doi          = {10.1007/978-3-319-23344-4\_26},
  timestamp    = {Sat, 09 Apr 2022 12:45:05 +0200},
  biburl       = {https://dblp.org/rec/conf/brain/OkazakiMSMM15.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/NakashoFOS14,
  author       = {Kazuhisa Nakasho and
                  Yuichi Futa and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Rank of Submodule, Linear Transformations and Linearly Independent
                  Subsets of Z-module},
  journal      = {Formaliz. Math.},
  volume       = {22},
  number       = {3},
  pages        = {189--198},
  year         = {2014},
  url          = {https://doi.org/10.2478/forma-2014-0021},
  doi          = {10.2478/FORMA-2014-0021},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/NakashoFOS14.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/AraiWO14,
  author       = {Kenichi Arai and
                  Ken Wakabayashi and
                  Hiroyuki Okazaki},
  title        = {Difference of Function on Vector Space over {F}},
  journal      = {Formaliz. Math.},
  volume       = {22},
  number       = {3},
  pages        = {269--275},
  year         = {2014},
  url          = {https://doi.org/10.2478/forma-2014-0027},
  doi          = {10.2478/FORMA-2014-0027},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/AraiWO14.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/FutaONS14,
  author       = {Yuichi Futa and
                  Hiroyuki Okazaki and
                  Kazuhisa Nakasho and
                  Yasunari Shidama},
  title        = {Torsion Z-module and Torsion-free Z-module},
  journal      = {Formaliz. Math.},
  volume       = {22},
  number       = {4},
  pages        = {277--289},
  year         = {2014},
  url          = {https://doi.org/10.2478/forma-2014-0028},
  doi          = {10.2478/FORMA-2014-0028},
  timestamp    = {Fri, 10 Dec 2021 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/FutaONS14.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/aires/OkazakiFS13,
  author       = {Hiroyuki Okazaki and
                  Yuichi Futa and
                  Yasunari Shidama},
  title        = {Formal definition of probability on finite and discrete sample space
                  for proving security of cryptographic systems using Mizar},
  journal      = {Artif. Intell. Res.},
  volume       = {2},
  number       = {4},
  pages        = {37--48},
  year         = {2013},
  url          = {https://doi.org/10.5430/air.v2n4p37},
  doi          = {10.5430/AIR.V2N4P37},
  timestamp    = {Wed, 10 Feb 2021 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/aires/OkazakiFS13.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/KanazashiOS13,
  author       = {Katuhiko Kanazashi and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {The Ck Space},
  journal      = {Formaliz. Math.},
  volume       = {21},
  number       = {1},
  pages        = {25--31},
  year         = {2013},
  url          = {https://doi.org/10.2478/forma-2013-0002},
  doi          = {10.2478/FORMA-2013-0002},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/KanazashiOS13.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/OkazakiS13,
  author       = {Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Random Variables and Product of Probability Spaces},
  journal      = {Formaliz. Math.},
  volume       = {21},
  number       = {1},
  pages        = {33--39},
  year         = {2013},
  url          = {https://doi.org/10.2478/forma-2013-0003},
  doi          = {10.2478/FORMA-2013-0003},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/OkazakiS13.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/OkazakiYS13,
  author       = {Hiroyuki Okazaki and
                  Hiroshi Yamazaki and
                  Yasunari Shidama},
  title        = {Isomorphisms of Direct Products of Finite Commutative Groups},
  journal      = {Formaliz. Math.},
  volume       = {21},
  number       = {1},
  pages        = {65--74},
  year         = {2013},
  url          = {https://doi.org/10.2478/forma-2013-0007},
  doi          = {10.2478/FORMA-2013-0007},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/OkazakiYS13.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/AraiO13,
  author       = {Kenichi Arai and
                  Hiroyuki Okazaki},
  title        = {N-Dimensional Binary Vector Spaces},
  journal      = {Formaliz. Math.},
  volume       = {21},
  number       = {2},
  pages        = {75--81},
  year         = {2013},
  url          = {https://doi.org/10.2478/forma-2013-0008},
  doi          = {10.2478/FORMA-2013-0008},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/AraiO13.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/FutaOMS13,
  author       = {Yuichi Futa and
                  Hiroyuki Okazaki and
                  Daichi Mizushima and
                  Yasunari Shidama},
  title        = {Gaussian Integers},
  journal      = {Formaliz. Math.},
  volume       = {21},
  number       = {2},
  pages        = {115--125},
  year         = {2013},
  url          = {https://doi.org/10.2478/forma-2013-0013},
  doi          = {10.2478/FORMA-2013-0013},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/FutaOMS13.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/OkazakiFS13,
  author       = {Hiroyuki Okazaki and
                  Yuichi Futa and
                  Yasunari Shidama},
  title        = {Constructing Binary Huffman Tree},
  journal      = {Formaliz. Math.},
  volume       = {21},
  number       = {2},
  pages        = {133--143},
  year         = {2013},
  url          = {https://doi.org/10.2478/forma-2013-0015},
  doi          = {10.2478/FORMA-2013-0015},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/OkazakiFS13.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/EndouOS13,
  author       = {Noboru Endou and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Double Sequences and Limits},
  journal      = {Formaliz. Math.},
  volume       = {21},
  number       = {3},
  pages        = {163--170},
  year         = {2013},
  url          = {https://doi.org/10.2478/forma-2013-0018},
  doi          = {10.2478/FORMA-2013-0018},
  timestamp    = {Sun, 12 Feb 2023 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/EndouOS13.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/AraiO13a,
  author       = {Kenichi Arai and
                  Hiroyuki Okazaki},
  title        = {Formalization of the Advanced Encryption Standard. Part {I}},
  journal      = {Formaliz. Math.},
  volume       = {21},
  number       = {3},
  pages        = {171--184},
  year         = {2013},
  url          = {https://doi.org/10.2478/forma-2013-0019},
  doi          = {10.2478/FORMA-2013-0019},
  timestamp    = {Mon, 28 Aug 2023 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/AraiO13a.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/YamazakiONS13,
  author       = {Hiroshi Yamazaki and
                  Hiroyuki Okazaki and
                  Kazuhisa Nakasho and
                  Yasunari Shidama},
  title        = {Isomorphisms of Direct Products of Cyclic Groups of Prime Power Order},
  journal      = {Formaliz. Math.},
  volume       = {21},
  number       = {3},
  pages        = {207--211},
  year         = {2013},
  url          = {https://doi.org/10.2478/forma-2013-0022},
  doi          = {10.2478/FORMA-2013-0022},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/YamazakiONS13.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/FutaOS13,
  author       = {Yuichi Futa and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Submodule of free Z-module},
  journal      = {Formaliz. Math.},
  volume       = {21},
  number       = {4},
  pages        = {273--282},
  year         = {2013},
  url          = {https://doi.org/10.2478/forma-2013-0029},
  doi          = {10.2478/FORMA-2013-0029},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/FutaOS13.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/jar/FutaOS13,
  author       = {Yuichi Futa and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Formalization of Definitions and Theorems Related to an Elliptic Curve
                  Over a Finite Prime Field by Using Mizar},
  journal      = {J. Autom. Reason.},
  volume       = {50},
  number       = {2},
  pages        = {161--172},
  year         = {2013},
  url          = {https://doi.org/10.1007/s10817-012-9265-2},
  doi          = {10.1007/S10817-012-9265-2},
  timestamp    = {Wed, 02 Sep 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/jar/FutaOS13.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/KanazashiOS12,
  author       = {Katuhiko Kanazashi and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Functional Space \emph{C}({\(\omega\)}), \emph{C}\({}_{\mbox{0}}\)({\(\omega\)})},
  journal      = {Formaliz. Math.},
  volume       = {20},
  number       = {1},
  pages        = {15--22},
  year         = {2012},
  url          = {https://doi.org/10.2478/v10037-012-0003-3},
  doi          = {10.2478/V10037-012-0003-3},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/KanazashiOS12.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/FutaOS12,
  author       = {Yuichi Futa and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Z-modules},
  journal      = {Formaliz. Math.},
  volume       = {20},
  number       = {1},
  pages        = {47--59},
  year         = {2012},
  url          = {https://doi.org/10.2478/v10037-012-0007-z},
  doi          = {10.2478/V10037-012-0007-Z},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/FutaOS12.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/FutaOMS12,
  author       = {Yuichi Futa and
                  Hiroyuki Okazaki and
                  Daichi Mizushima and
                  Yasunari Shidama},
  title        = {Operations of Points on Elliptic Curve in Projective Coordinates},
  journal      = {Formaliz. Math.},
  volume       = {20},
  number       = {1},
  pages        = {87--95},
  year         = {2012},
  url          = {https://doi.org/10.2478/v10037-012-0012-2},
  doi          = {10.2478/V10037-012-0012-2},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/FutaOMS12.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/EndouOS12,
  author       = {Noboru Endou and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Higher-Order Partial Differentiation},
  journal      = {Formaliz. Math.},
  volume       = {20},
  number       = {2},
  pages        = {113--124},
  year         = {2012},
  url          = {https://doi.org/10.2478/v10037-012-0015-z},
  doi          = {10.2478/V10037-012-0015-Z},
  timestamp    = {Sun, 12 Feb 2023 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/EndouOS12.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/OkazakiS12,
  author       = {Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Formalization of the Data Encryption Standard},
  journal      = {Formaliz. Math.},
  volume       = {20},
  number       = {2},
  pages        = {125--146},
  year         = {2012},
  url          = {https://doi.org/10.2478/v10037-012-0016-y},
  doi          = {10.2478/V10037-012-0016-Y},
  timestamp    = {Mon, 28 Aug 2023 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/OkazakiS12.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/OkazakiAS12,
  author       = {Hiroyuki Okazaki and
                  Yosiki Aoki and
                  Yasunari Shidama},
  title        = {Extended Euclidean Algorithm and {CRT} Algorithm},
  journal      = {Formaliz. Math.},
  volume       = {20},
  number       = {2},
  pages        = {175--179},
  year         = {2012},
  url          = {https://doi.org/10.2478/v10037-012-0020-2},
  doi          = {10.2478/V10037-012-0020-2},
  timestamp    = {Mon, 03 Jan 2022 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/OkazakiAS12.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/FutaOS12a,
  author       = {Yuichi Futa and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Quotient Module of Z-module},
  journal      = {Formaliz. Math.},
  volume       = {20},
  number       = {3},
  pages        = {205--214},
  year         = {2012},
  url          = {https://doi.org/10.2478/v10037-012-0024-y},
  doi          = {10.2478/V10037-012-0024-Y},
  timestamp    = {Mon, 03 Jan 2022 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/FutaOS12a.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/Okazaki12,
  author       = {Hiroyuki Okazaki},
  title        = {Posterior Probability on Finite Set},
  journal      = {Formaliz. Math.},
  volume       = {20},
  number       = {4},
  pages        = {257--263},
  year         = {2012},
  url          = {https://doi.org/10.2478/v10037-012-0030-0},
  doi          = {10.2478/V10037-012-0030-0},
  timestamp    = {Fri, 10 Dec 2021 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/Okazaki12.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/SakuraiOS12,
  author       = {Hideki Sakurai and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Banach's Continuous Inverse Theorem and Closed Graph Theorem},
  journal      = {Formaliz. Math.},
  volume       = {20},
  number       = {4},
  pages        = {271--274},
  year         = {2012},
  url          = {https://doi.org/10.2478/v10037-012-0032-y},
  doi          = {10.2478/V10037-012-0032-Y},
  timestamp    = {Mon, 03 Jan 2022 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/SakuraiOS12.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/FutaOS12b,
  author       = {Yuichi Futa and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Free {\(\mathbb{Z}\)}-module},
  journal      = {Formaliz. Math.},
  volume       = {20},
  number       = {4},
  pages        = {275--280},
  year         = {2012},
  url          = {https://doi.org/10.2478/v10037-012-0033-x},
  doi          = {10.2478/V10037-012-0033-X},
  timestamp    = {Mon, 03 Jan 2022 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/FutaOS12b.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/AraiOS12,
  author       = {Kenichi Arai and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Isomorphisms of Direct Products of Finite Cyclic Groups},
  journal      = {Formaliz. Math.},
  volume       = {20},
  number       = {4},
  pages        = {343--347},
  year         = {2012},
  url          = {https://doi.org/10.2478/v10037-012-0038-5},
  doi          = {10.2478/V10037-012-0038-5},
  timestamp    = {Mon, 03 Jan 2022 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/AraiOS12.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/isita/FutaMO12,
  author       = {Yuichi Futa and
                  Daichi Mizushima and
                  Hiroyuki Okazaki},
  title        = {Formalization of Gaussian integers, Gaussian rational numbers, and
                  their algebraic structures with Mizar},
  booktitle    = {Proceedings of the International Symposium on Information Theory and
                  its Applications, {ISITA} 2012, Honolulu, HI, USA, October 28-31,
                  2012},
  pages        = {591--595},
  publisher    = {{IEEE}},
  year         = {2012},
  url          = {https://ieeexplore.ieee.org/document/6401006/},
  timestamp    = {Wed, 11 Aug 2021 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/conf/isita/FutaMO12.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/OkazakiAS11,
  author       = {Hiroyuki Okazaki and
                  Kenichi Arai and
                  Yasunari Shidama},
  title        = {Normal Subgroup of Product of Groups},
  journal      = {Formaliz. Math.},
  volume       = {19},
  number       = {1},
  pages        = {23--26},
  year         = {2011},
  url          = {https://doi.org/10.2478/v10037-011-0004-7},
  doi          = {10.2478/V10037-011-0004-7},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/OkazakiAS11.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/OkazakiES11,
  author       = {Hiroyuki Okazaki and
                  Noboru Endou and
                  Yasunari Shidama},
  title        = {More on Continuous Functions on Normed Linear Spaces},
  journal      = {Formaliz. Math.},
  volume       = {19},
  number       = {1},
  pages        = {45--49},
  year         = {2011},
  url          = {https://doi.org/10.2478/v10037-011-0008-3},
  doi          = {10.2478/V10037-011-0008-3},
  timestamp    = {Sun, 12 Feb 2023 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/OkazakiES11.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/OkazakiES11a,
  author       = {Hiroyuki Okazaki and
                  Noboru Endou and
                  Yasunari Shidama},
  title        = {Cartesian Products of Family of Real Linear Spaces},
  journal      = {Formaliz. Math.},
  volume       = {19},
  number       = {1},
  pages        = {51--59},
  year         = {2011},
  url          = {https://doi.org/10.2478/v10037-011-0009-2},
  doi          = {10.2478/V10037-011-0009-2},
  timestamp    = {Sun, 12 Feb 2023 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/OkazakiES11a.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/FutaOS11,
  author       = {Yuichi Futa and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Formalization of Integral Linear Space},
  journal      = {Formaliz. Math.},
  volume       = {19},
  number       = {1},
  pages        = {61--64},
  year         = {2011},
  url          = {https://doi.org/10.2478/v10037-011-0010-9},
  doi          = {10.2478/V10037-011-0010-9},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/FutaOS11.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/OkazakiENS11,
  author       = {Hiroyuki Okazaki and
                  Noboru Endou and
                  Keiko Narita and
                  Yasunari Shidama},
  title        = {Differentiable Functions into Real Normed Spaces},
  journal      = {Formaliz. Math.},
  volume       = {19},
  number       = {2},
  pages        = {69--72},
  year         = {2011},
  url          = {https://doi.org/10.2478/v10037-011-0012-7},
  doi          = {10.2478/V10037-011-0012-7},
  timestamp    = {Sun, 12 Feb 2023 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/OkazakiENS11.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/KanazashiOS11,
  author       = {Katuhiko Kanazashi and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Banach Algebra of Bounded Complex-Valued Functionals},
  journal      = {Formaliz. Math.},
  volume       = {19},
  number       = {2},
  pages        = {121--126},
  year         = {2011},
  url          = {https://doi.org/10.2478/v10037-011-0019-0},
  doi          = {10.2478/V10037-011-0019-0},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/KanazashiOS11.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/FutaOS11a,
  author       = {Yuichi Futa and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Set of Points on Elliptic Curve in Projective Coordinates},
  journal      = {Formaliz. Math.},
  volume       = {19},
  number       = {3},
  pages        = {131--138},
  year         = {2011},
  url          = {https://doi.org/10.2478/v10037-011-0021-6},
  doi          = {10.2478/V10037-011-0021-6},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/FutaOS11a.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/OkazakiS10,
  author       = {Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Probability Measure on Discrete Spaces and Algebra of Real-Valued
                  Random Variables},
  journal      = {Formaliz. Math.},
  volume       = {18},
  number       = {1-4},
  pages        = {213--217},
  year         = {2010},
  url          = {https://doi.org/10.2478/v10037-010-0026-6},
  doi          = {10.2478/V10037-010-0026-6},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/OkazakiS10.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/fcs/AraiKO10,
  author       = {Kenichi Arai and
                  Nobuaki Kondo and
                  Hiroyuki Okazaki},
  editor       = {Hamid R. Arabnia and
                  George A. Gravvanis and
                  Ashu M. G. Solo},
  title        = {Formalization of Probability and Random Sampling on a Finite and Discrete
                  Sample Space Using the Mizar Proof Checker},
  booktitle    = {Proceedings of the 2010 International Conference on Foundations of
                  Computer Science, {FCS} 2010, July 12-15, 2010, Las Vegas, Nevada,
                  {USA}},
  pages        = {81--86},
  publisher    = {{CSREA} Press},
  year         = {2010},
  timestamp    = {Wed, 08 Dec 2010 08:03:41 +0100},
  biburl       = {https://dblp.org/rec/conf/fcs/AraiKO10.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/OkazakiS09,
  author       = {Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Probability on Finite Set and Real-Valued Random Variables},
  journal      = {Formaliz. Math.},
  volume       = {17},
  number       = {1-4},
  pages        = {129--136},
  year         = {2009},
  url          = {https://doi.org/10.2478/v10037-009-0014-x},
  doi          = {10.2478/V10037-009-0014-X},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/OkazakiS09.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/AraiO09,
  author       = {Kenichi Arai and
                  Hiroyuki Okazaki},
  title        = {Properties of Primes and Multiplicative Group of a Field},
  journal      = {Formaliz. Math.},
  volume       = {17},
  number       = {1-4},
  pages        = {151--155},
  year         = {2009},
  url          = {https://doi.org/10.2478/v10037-009-0017-7},
  doi          = {10.2478/V10037-009-0017-7},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/AraiO09.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/EndouOS09,
  author       = {Noboru Endou and
                  Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Hopf Extension Theorem of Measure},
  journal      = {Formaliz. Math.},
  volume       = {17},
  number       = {1-4},
  pages        = {157--162},
  year         = {2009},
  url          = {https://doi.org/10.2478/v10037-009-0018-6},
  doi          = {10.2478/V10037-009-0018-6},
  timestamp    = {Sun, 12 Feb 2023 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/fm/EndouOS09.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/Okazaki09,
  author       = {Hiroyuki Okazaki},
  title        = {Probability on Finite and Discrete Set and Uniform Distribution},
  journal      = {Formaliz. Math.},
  volume       = {17},
  number       = {1-4},
  pages        = {173--178},
  year         = {2009},
  url          = {https://doi.org/10.2478/v10037-009-0020-z},
  doi          = {10.2478/V10037-009-0020-Z},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/Okazaki09.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/fm/OkazakiS08,
  author       = {Hiroyuki Okazaki and
                  Yasunari Shidama},
  title        = {Uniqueness of Factoring an Integer and Multiplicative Group Z/pZ*},
  journal      = {Formaliz. Math.},
  volume       = {16},
  number       = {1-4},
  pages        = {103--107},
  year         = {2008},
  url          = {https://doi.org/10.2478/v10037-008-0015-1},
  doi          = {10.2478/V10037-008-0015-1},
  timestamp    = {Thu, 18 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/fm/OkazakiS08.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/gecco/AguirreOF07,
  author       = {Hern{\'{a}}n E. Aguirre and
                  Hiroyuki Okazaki and
                  Yasushi Fuwa},
  editor       = {Hod Lipson},
  title        = {An evolutionary multiobjective approach to design highly non-linear
                  Boolean functions},
  booktitle    = {Genetic and Evolutionary Computation Conference, {GECCO} 2007, Proceedings,
                  London, England, UK, July 7-11, 2007},
  pages        = {749--756},
  publisher    = {{ACM}},
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  editor       = {Masayoshi Ejiri and
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  title        = {Distributed Self-Healing Control in {SONET}},
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