Simplification of transition systems with the use of lazy Kleene algebras

• Project/Area Number: 22500016
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Fundamental theory of informatics
• Research Institution: Kagoshima University
• Principal Investigator: FURUSAWA Hitoshi 鹿児島大学, 大学院・理工学研究科, 准教授 (00357930)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: プログラム理論 / べき集合的半束 / 緩クリーニ代数 / べき等半環 / 半束 / 表現定理 / イデアル完備化 / べき等左半環 / *イデアル / クリーニの定理

Research Abstract

The following results on relationship between subclasses of lazy Kleene algebras and relational description of transition modelsare obtained.
（１）a sufficient condition to give an adjunction between the category of ＊-continuous idempotent left semirings and the category of D-continuous idempotent left semirings by a kind of ideal completion
２）relational and multirelational representation theorems for complete idempotent left semirings
（３）a necessary and sufficient condition for a quantale to have quantale-homomorphic embedding into a quantale consisting of the set of all binary relations on some set

Research Products

• [Journal Article] Relational Representation Theorem for Powerset Quantales, In Wolfram Kahl and Timothy G. Griffin eds., Relational and Algebraic Methods in Computer Science (2012)
  • Author(s): Nishizawa, Koki and Furusawa, Hitoshi
  • Journal Title: 13th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2012, Cambridge, UK Volume: LNCS 7560 Pages: 207-218
  • DOI: 10.1007/978-3-642-33314-9_14
  • ISBN: 9783642333132, 9783642333149
  • Peer Reviewed
• [Journal Article] Ideal Completion of Join Semilattice over T-algebra (2012)
  • Author(s): Nishizawa, Koki. and Furusawa, Hitoshi
  • Journal Title: Bulletin of Tottori University of Environmental Studies Volume: Vol. 9 and 10 Pages: 91-103
  • NAID: 40019237804
  • URL: http://www.kankyo-u.ac.jp/f/845/bulletin/009-010/091-103.pdf
  • Peer Reviewed
• [Journal Article] Point Axioms in Dedekind Categories (2012)
  • Author(s): 古澤仁，河原康雄
  • Journal Title: Lecture Notes in Computer Science, Springer Volume: 7560 Pages: 219-234
  • DOI: 10.1007/978-3-642-33314-9_15
  • ISBN: 9783642333132, 9783642333149
  • Peer Reviewed
• [Journal Article] Continuous Relations and Richardson's Theorem (2012)
  • Author(s): 古澤仁，石田俊一，河原康雄
  • Journal Title: Lecture Notes in Computer Science, Springer Volume: 7560 Pages: 310-325
  • DOI: 10.1007/978-3-642-33314-9_21
  • ISBN: 9783642333132, 9783642333149
  • Peer Reviewed
• [Journal Article] Ideal Completion of Join Semilattice over T-algebra (2012)
  • Author(s): 西澤弘毅, 古澤仁
  • Journal Title: Bulletin of Tottori University of Environmental Studies Volume: 9・10 Pages: 91-103
  • NAID: 40019237804
  • Peer Reviewed
• [Journal Article] Remarks on Ideal Completion of *-Continuous Idempotent Left Semirings (2011)
  • Author(s): Furusawa, Hitoshi, Sanda, Fumiya. and Tsumagari, Norihiro
  • Journal Title: Bulletin of Informatics and Cybernetics Volume: Vol. 43 Pages: 1-21
  • NAID: 120005397797
  • Peer Reviewed
• [Journal Article] Relational and Multirelational Representation Theorems for Complete Idempotent Left Semirings (2011)
  • Author(s): Hitoshi Furusawa, Koki Nishizawa
  • Journal Title: Lecture Notes in Computer Science, Springer Volume: 6663 Pages: 148-163
  • DOI: 10.1007/978-3-642-21070-9_13
  • ISBN: 9783642210693, 9783642210709
  • Peer Reviewed
• [Journal Article] Remarks on Ideal Completion of ^*-Continuous Idempotent Left Semirings (2011)
  • Author(s): 古澤仁, 三田文也, 津曲紀宏
  • Journal Title: Bulletin of Informatics and Cybernetics Volume: 43 Pages: 1-21
  • NAID: 120005397797
  • Peer Reviewed
• [Journal Article] Dedekind Categories with cutoff operators (2011)
  • Author(s): Hitoshi Furusawa, Yasuo Kawahara, Michael Winter
  • Journal Title: Fuzzy Sets and Systems Volume: 173 Issue: 1 Pages: 1-24
  • DOI: 10.1016/j.fss.2010.11.008
  • Peer Reviewed
• [Journal Article] Dedekind Categories with cutoff operators
  • Author(s): 古澤仁, 河原康雄, Michael Winter
  • Journal Title: Fuzzy Sets and Systems Volume: (印刷中)
  • Peer Reviewed
• [Journal Article] Relational and Multirelational Representation Theorems for Complete Idempotent Left Semirings
  • Author(s): 古澤仁, 西澤弘毅
  • Journal Title: Lecture Notes in Computer Science Volume: (印刷中)
  • Peer Reviewed
• [Journal Article] Remarks on Ideal Completion of ^*-continuous Idempotent Left Semirings
  • Author(s): 古澤仁, 三田文也, 津曲紀宏
  • Journal Title: Bulletin of Informatics and Cybernetics Volume: (掲載決定)
  • NAID: 120005397797
  • Peer Reviewed
• [Presentation] 完備べき等左半環-二項多重関係による表現を中心に- (2011)
  • Author(s): 古澤仁
  • Organizer: 南九州代数系集会
  • Place of Presentation: 鹿児島大学(鹿児島市)
  • Year and Date: 2011-08-26
• [Presentation] Relational and Multirelational Representation Theorems for Complete Idempotent Left Semirings (2011)
  • Author(s): Hitoshi Furusaw
  • Organizer: 12th International Conference on Relational and Algebraic Methods in Computer Science (RAMiCS 2011)
  • Place of Presentation: Rotterdam, The Netherlands
  • Year and Date: 2011-06-01
• [Presentation] Relational and Multirelational Representation Theorems for Complete Idempotent Left Semirings (2011)
  • Author(s): 古澤仁
  • Organizer: 12th International Conference on Relational and Algebraic Methods in Computer Science
  • Place of Presentation: Erasmus University Rotterdam(オランダ,ロッテルダム)
  • Year and Date: 2011-06-01
• [Presentation] 任意の上限について素な完備べき等左半環の多重関係による表現 (2010)
  • Author(s): 古澤仁
  • Organizer: 第6回論理と計算に関するセミナー
  • Place of Presentation: 九州大学(福岡市)
  • Year and Date: 2010-11-20
• [Presentation] Representation theorems for complete idempotent left semirings, Workshop on Lattices (2010)
  • Author(s): Hitoshi Furusawa
  • Organizer: Relations and Kleene Algebras
  • Place of Presentation: London, UK
  • Year and Date: 2010-09-21
• [Presentation] Representation Theorems for Complete Idempotent Left Semirings (2010)
  • Author(s): 古澤仁
  • Organizer: Workshop on Lattices, Relations and Kleene Algebras
  • Place of Presentation: University College London(イギリス, ロンドン)
  • Year and Date: 2010-09-21
• [Presentation] 完備べき等左半環の表現定理 (2010)
  • Author(s): 古澤仁
  • Organizer: 第5回論理と計算に関するセミナー
  • Place of Presentation: 九州大学(福岡市)
  • Year and Date: 2010-07-23
• [Presentation] Continuous Relations and Richardson's Theorem
  • Author(s): 古澤仁
  • Organizer: 13th International Conference on Relational and Algebraic Methods in Computer Science
  • Place of Presentation: ケンブリッジ（イギリス）
• [Presentation] Point Axioms in Dedekind Categories
  • Author(s): 古澤仁
  • Organizer: 13th International Conference on Relational and Algebraic Methods in Computer Science
  • Place of Presentation: ケンブリッジ（イギリス）
• [Presentation] 完備べき等左半環の多重関係による表現
  • Author(s): 古澤仁
  • Organizer: 数学の形式化に関する研究集会
  • Place of Presentation: 福岡市
• [Remarks]
  • URL: http://www.sci.kagoshima-u.ac.jp/furusawa/person/research.html
• [Remarks] 個人ホームページ
  • URL: http://www.sci.kagoshima-u.ac.jp/~furusawa/person/research.html
• [Remarks]
  • URL: http://www.sci.kagoshima-u.ac.jp/~furusawa/person/research.html
• [Remarks]
  • URL: http://www.sci.kagoshima-u.ac.jp/~furusawa/person/research.html