半群,形式言語及び計算理論の研究

1997 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): 近藤 通朗 島根大学, 総合理工学部, 助教授 (40211916) ; NEHANIV C. 会津大学, コンピュータ理工学部, 教授 (10254054) ; 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) ; 伊藤 正美 京都産業大学, 理学部, 教授 (50065843)
• Keywords: semigroup / representation / amalgamation / formal language / rewriting system / free monoid / automata / computation

Research Abstract

平成9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tansitive & effective表現の特徴づけを行い、それを用いて、一般化された逆〔*〕半群のamalgamが埋め込まれることを証明した。
(2)オメガ集合の概念を導入して、Reillyの表現を一般化された半群の表現に拡張した。
(3)言語上のshuffle積及びその逆演算の種々の性質を形式言語学的視点から調べた。
(4)2つのペトリネトの融合を定義し、それがペトリネト言語にどう反映するかを研究した。
(5)Acetoのconjectureを否定的に解決した。
(6)自由モノイド上のmorphismのrepetitivenessがpolynomial time決定されることを証明した。
(7)Hilbert algebrasとpositive implicative algebrasの間にはdual isomorphismが存在することを示した。このことより、これら2つの代数系は同じ代数構造を持つことがわかる。
2.当研究課題に関連して2回研究集会を開き、それらの報告集を作成した。
(1)Proceedings of the Workshop on Languages,Computation and Algebra,edited by T.Imaoka,27-28August,1997,Kobe University,89p.,(1997)
(2)Proceedings of the First Symposium on Algebra,Languages and Computation,edited by T.Imaoka & C.Nehaniv,30 October-1 November,1997,University of Aizu,99p.,(1998).

Research Products

• [Publications] T.E.Hall & T,Imaoka: "Representations and amalgamation of generalized inverse ^*-semigroups" Semigroup Forum. (発表予定).
• [Publications] M.Ito, L.Kari & G.Thierrin: "Shuffle and scattered deletion closure of languages" Theoretical Computer Science. (発表予定).
• [Publications] M.Ito, F.Tiplea & M.Katsura: "On replacement of Petri nets" Acta Informatica. (発表予定).
• [Publications] Y.Kobayashi & F.Otto: "Repetitiveness of DOL-languages is decidable in polynomial time" MFCS'97,Lect.Notes Comp.Sci.1295. 337-346 (1997)
• [Publications] P.Domosi & C.Nehaniv: "Algebraic theory of finite automata" Mathematica Japonica. (発表予定).
• [Publications] M.Kondo: "Hilbert algebras are dual isomorphic to positive implicative BCK-algebras" Mathematica Japonica. (発表予定).
• [Publications] T.Imaoka & T.Ogawa: "Some remarks on representations of generalized inverse *-semigroups" Mem.Fac.Sci.Eng.Shimane Univ,Series B. 30. 23-35 (1997)
• [Publications] T.Imaoka & M.Katsura: "Representations of locally inverse *-semigroups II" Semigroup Forum. 55. 247-255 (1997)
• [Publications] M.Ito & B.Imreh: "On di-product of nondeterministic automata" Algebra Colloquium. 4. 195-202 (1997)
• [Publications] M.Ito & L.Kari: "Insertion and deletion closure of languages" Theoretical Computer Science. 183. 3-19 (1997)
• [Publications] M.Ito, F.Tiplea & M.Katsura: "Processes and vectoral characterizations of parallel communicating grammar systems" Jounal of Automata,Languages and Combinatorics. 2. 47-73 (1997)
• [Publications] M.Ito & P.Domosi: "Characterization of languages by lengths of their subwords" Monograph Series(Springer-Verlag,Singapore). (発表予定).
• [Publications] M.Ito, Z.Esik & M.Katsura: "The equational theory of reversal" Algebraic Engineering. (発表予定).
• [Publications] M.Ito: "Shuffle products and related operations on languages" Algebraic Engineering. (発表予定).
• [Publications] M.Katsura: "On a conjecture by L.Aceto" Proc.1st Sympo.on Algebra,Languages & Computation. 13-14 (1998)
• [Publications] M.Katsura & Y.Kobayashi: "Constructing finitely presented monoids which have no finite complete presentation" Semigroup Forum. 54. 292-302 (1997)
• [Publications] K.Tsuji, M.Katsura & Y.Kobayashi: "On termination of confluent one-rule string-rewriting systems" Inform.Process.Let.61. 91-96 (1997)
• [Publications] F.Otto & Y.Kobayashi: "Properties of monoids that are presented by finite convergent string-rewriting system -a servey-" Advances in Algorithms,Languages and Conplexity. 226-266 (1997)
• [Publications] F.Otto, M.Katsura & Y.Kobayashi: "Cross-sections for finitely presented monoids with decidable word problems" RTA'97,Lect.Notes Comp.Sci.,Springer. 1232. 53-67 (1997)
• [Publications] Y.Kobayashi, F.Otto & P.Seebold: "A complete characterization of repetitive morphisms over the two-letter alphabet" COCOON'97,Lect.Notes Comp.Sci.,Springer. 1278. 393-402 (1997)
• [Publications] M.Kondo: "Conditions for L(X) to be an ideal in BCI-algebras" Math.Japonica. 46. 237-239 (1997)
• [Publications] M.Kondo: "Congruences and closed ideals in BCI-algebras" Math.Japonica. 46. 491-496 (1997)
• [Publications] M.Kondo: "Duality theorem for p-semisimple BCI-algebras" Math.Japonica. 46. 497-501 (1997)
• [Publications] M.Kondo: "Functional freeness for the Berm an class Kmn of Ockham algebras" Mem.Fac.Sci.Eng,Shimane Univ.,Series B. 30. 49-55 (1997)
• [Publications] M.Kondo: "Note on BCI-G part of BCI-algebras" Math.Japonica. (発表予定).
• [Publications] M.Kondo: "Annihilators in BCK-algebras" Math.Japonica. (発表予定).
• [Publications] P.Domosi & C.Nehaniv: "Some results and ploblems on finite homogeneous automata networks" Proc.Workshop on Languages,Computation and Algebra. 1-11 (1997)
• [Publications] P.Domosi & C.Nehaniv: "Finite automata networks and products of automata" Proc.1st Sympo.on Algebra,Languages and Computation. 69-76 (1998)
• [Publications] C.Nehaniv & K.Dautenhahn: "Semigroup expansions for autobiographic agents" Proc.1st Sympo.on Algebra,Languages and Computation. 77-84 (1998)
• [Publications] K.Dautenhahn & C.Nehaniv: "Artificial lite and natural stories" Proc.3rd Internat.Sympo.on Artificial life and Robotics. 435-439 (1998)
• [Publications] T.Imaoka(編著): "Proceedings of the Workshop on Languages,Computation and Algebra" 89 (1997)
• [Publications] T.Imaoka & C.Nehaniv(編著): "Proceedings of the 1^<st> Symposium on Algebra,Languages and Computation" 99 (1998)