半群、形式言語及び計算理論の研究

1999 Fiscal Year Annual Research Report

• Project/Area Number: 09440017
• Research Institution: Shimane University
• Principal Investigator: 今岡 輝男 島根大学, 総合理工学部, 教授 (60032603)
• Co-Investigator(Kenkyū-buntansha): 伊藤 正美 京都産業大学, 理学部, 教授 (50065843) ; 近藤 通朗 島根大学, 総合理工学部, 助教授 (40211916) ; 庄司 邦孝 島根大学, 総合理工学部, 教授 (50093646) ; 小林 ゆう治 東邦大学, 理学部, 教授 (70035343) ; 勝良 昌司 京都産業大学, 理学部, 教授 (80065870)
• Keywords: semigroup / representation / amalgamation / formal language / rewriting system / free monoid / automata / computation

Research Abstract

平成11年度の研究実績は以下の通りである.
1.主な研究成果
(1)一般化された逆*半群の族が強融合性を持つことを一般化された逆*半群の表現を導入して証明した.
(2)一般化された逆*半群のtransitive表現をright ω-cosetを用いて特徴付けた.
(3)有限半群がrepresentation extension propertyを持つかどうかという問題は決定可能であることを証明した.
(4)複数のPetri netを発火系列として言語の性質を保ちながらある種の標準形になるように繋ぐ方法を与えた.
(5)言語の混合削除剰余演算を定義し,その性質及び最大混合削除剰余閉包の存在条件を求めた.
(6)3種類の非決定性有向オートマトンの定義を与え,それによって決定される言語の属の包含関係を調べた.また,これら3種類の定義は決定性オートマトンの場合には一致する.
2.研究集会
(1)The 3rd Symposium on Algebra,Languages and Computation,大阪大学,1999年8月3日-4日(責任者:今岡輝男)この研究集会は等研究課題に関連して開催され,その報告集を作成した.また,これをWeb上でも閲覧できるようにした.
(2)The 3rd International Colloquium on Words,Languages and Combinatorics III,京都産業大学,2000年3月14日-18日(責任者:伊藤正美,今岡輝男)

Research Products

• [Publications] T.Imaoka and I.Inata: "Representations of generalized inverse *-semigroups by right ω-cosets"Math.Japonica. (to appear).
• [Publications] K.Shoji: "Decidability of the representation extension property for finite semigroups"Proc.Amer.Math.Soc.. (to appear).
• [Publications] M.Kondo: "On (*)-ideals in BCK-algebras"Math.Japonica. 50. 201-205 (1999)
• [Publications] M.Ito and B.Imreh: "A note on star-product"Acta Cybernetica. 14. 99-104 (1999)
• [Publications] M.Ito,M.Katsura and F.L.Tiplea: "On replacement of Petri nets and some applications"Acta Informatica. (to appear).
• [Publications] Y.Kobayashi and F.Otto: "Repetitiveness of languages generated by morphisms"Theoret.Comp.Sci.. (to appear).
• [Publications] T.E.Hall and T.Imaoka: "Representations and amalgamation of generalized inverse*-semigroups"Semigroup Forum. 58. 126-141 (1999)
• [Publications] V.Diekert and Y.Kobayashi: "Some identities related to automata,determinants and Mobius functions"Algebraic Engineering(edied by C.Nehaniv and M.Ito),Springer. 330-349 (1999)
• [Publications] M.Ito: "Shuffle products and related operations on languages"Algebraic Engineering(edied by C.Nehaniv and M.Ito),Springer. 484-493 (1999)
• [Publications] Z.Esik,M.Ito and M.Katsura: "The equational properties of reversal"Algebraic Engineering(edied by C.Nehaniv and M.Ito),Springer. 502-521 (1999)
• [Publications] M.Kondo: "Hilbert algebras are dual isomorphic to positive BCK-algebras"Math.Japonica. 49. 265-268 (1999)
• [Publications] M.Kondo: "Annihlators in BCK-algebras"Math.Japonica. 49. 407-410 (1999)
• [Publications] I.Inata and T.Imaoka: "Note on transitive representations of generalized inverse *-semigroups"RIMS Kokyuroku. 1106. 61-65 (1999)
• [Publications] B.Imreh and M.Ito: "Nondeterministic directable automata and related languages"RIMS Kokyuroku. 1106. 81-87 (1999)
• [Publications] M.Kondo: "Noe on the semantics of logic programming"RIMS Kokyuroku. 1106. 94-101 (1999)
• [Publications] K.Shoji: "Finite completely 0-simpl semigroups and amalgamation ases for finite semigroups"RIMS Kokyuroku. 1106. 211-212 (1999)
• [Publications] M.Kondo: "Axiomatic theory of bilattices in the senantics of artificial inteligence"Far.East J.Math Soc.. 2. 113-122 (1999)
• [Publications] M.Ito and L.Kari: "Shuffle and scattered deletion closure of languages"Theort.Compt.Sci.. (to appear).
• [Publications] T.Imaoka(編著): "Proceedings of the 3rd Symposium on Algebra,Languages and Computation"71 (2000)
• [Publications] M.Ito and T.Imaoka(編著): "Words,Languages and Combinatorics III"World Scientific,Singapore(to appear).
• [Publications] C.L.Nehaniv and M.Ito(編著): "Algebraic Engineering"World Scientific,Singapore. 554 (1999)
• [Publications] C.L.Nehaniv and M.Ito(編著): "Special Issue of Theoretical Computer Science"Elseviers,Amsterdam(to appear).