2017 Fiscal Year Final Research Report
Analysis of probabilistic systems by relational and algebraic methods
| Project/Area Number |
16K21557
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Theory of informatics
Foundations of mathematics/Applied mathematics
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| Research Institution | Sojo University |
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Principal Investigator |
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| Research Collaborator |
FURUSAWA Hitoshi 鹿児島大学, 大学院理工学研究科, 教授 (00357930)
KAWAHARA Yasuo 九州大学, 名誉教授 (90091181)
NISHIZAWA Koki 神奈川大学, 工学部, 准教授 (60455433)
STRUTH Georg University of Sheffield, Department of Computer Science, Professor
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| Project Period (FY) |
2016-04-01 – 2018-03-31
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| Keywords | 確率的システム / 意味論 / 関係理論 / 圏論 / 代数 |
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| Outline of Final Research Achievements |
(1) Extended the previous results [Tsumagari et al, JLAMP, 2014], we showed that convex composition of convex relations is associative. Because of not assuming totality, we introduced distribution subidentities. (2) We gave relational formalisations of Kleisli, Parikh and Peleg compositions and liftings of multirelations. These results contributed to improve the research (1) above. (3) We introduced Cantor category where is Dedekind category satisfying a few additional axiom, and relationally formulated the axiom of choice and Zorn’s lemma. (4)We generalised various multirelations to "V-relations on the category L" where L has powers and V is an object of L. They includes ordinary binary relation, binary multirelation, probabilistic relation. In addition, we gave the sufficient condition to compose two different types of V-relations.
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| Free Research Field |
理論計算機科学
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