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2000 Fiscal Year Final Research Report Summary

Formal Languages, Codes and Cryptosystems

Research Project

Project/Area Number 10440034
Research Category

Grant-in-Aid for Scientific Research (B).

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKyoto Sangyo University

Principal Investigator

ITO Masami  Kyoto Sangyo University, Mathematics, Professor, 理学部, 教授 (50065843)

Co-Investigator(Kenkyū-buntansha) ISHIDA Hisashi  Kyoto Sangyo University, Mathematics, Professor, 理学部, 教授 (10103714)
MURASE Atsushi  Kyoto Sangyo University, Mathematics, Professor, 理学部, 教授 (40157772)
KATSURA Masashi  Kyoto Sangyo University, Mathematics, Professor, 理学部, 教授 (80065870)
WASHIHARA Masako  Kyoto Sangyo University, Mathematics, Professor, 理学部, 教授 (40065800)
YASUGI Mariko  Kyoto Sangyo University, Computer Science, Professor, 理学部, 教授 (90022277)
Project Period (FY) 1998 – 2000
Keywordsprimitive word / context-free language / regular language / decidability problem / root(L) / deg(L) / palindrome / Petri net
Research Abstract

A word u is said to be primitive if u cannot be represented as the power of another word. By Q(X) we denote the set of all primitive words over X.It is conjectured that Q(X) is not context-free. However, this conjecture is still open. In our research, we investigate some decidability problems concerning Q(X) and its related languages. Let u ∈ X^+. If u = v^l for a positive integer l and a primitive word v, then we denote root (u) = v. For a language L ⊆ X^+, we define root(L) = ∪_<u∈L> root(u). Then we have the following results : (1) For a given regular (or context-free) language L ⊆ X^+, it is decidable whether root(L) is finite. (2) For a given regular language L ⊆ X^+, it is decidable whether root(L) is regular. (3) For a given context-free language L ⊆ X^+, it is undecidable whether root(L) is regular (or context-free). (4) For a given regular language L ⊆ X^+, it is decidable whether L ⊆ Q(X) holds. (5) For a given context-free language L ⊆ X^+, it is undecidable whether L ⊆ Q(X) holds.
Let L ⊆ X^+. Then, by deg(L) we mean the set {i : q ∈ Q(X), q^l ∈ L}. Then we have the following results : (1) For a given regular language L ⊆ X^+, it is decidable whether deg(L) is finite. (2) For a given context-free language L ⊆ X^+, it is undecidable whether deg(L) is finite.
A language L ⊆ X^+ is said to be palindromic if all words in L are palindromes. It is known that there is no dense palindromic regular language contained in Q(X). For the case of context-free palindromic languages, we have the same result and moreover we can prove that deg(L) is infinite (more exactly, aperiodic) if L ⊆ X^+ is a dense palindromic context-free language.
For the period between April 1, 1998 and March 31, 2001, we have also investigated deterministic and/or nondeterministic directable automata and related languages, some kinds of code-related Petri net languages etc.

  • Research Products

    (22 results)

All Other

All Publications (22 results)

  • [Publications] P.Domosi,M.Ito: "Characterization of languages by lengths of their subwords"Monograph Series (Springer). 117-129 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Ito,P.V.Silva: "Remarks on deletions, scattered deletions and related operations on languages"Semigroups and Applications (World Scientific). 95-105 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] B.Imreh,M.Ito: "A note on the star-product"Acta Cybernetica. 14. 99-104 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Ito: "Shuffle products and related operations on languages"Algebratc Engineering (World Scientific). 484-493 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] B.Imreh,M.Ito: "On some special classes of regular languages"Jewels are Forever (Springer). 25-34 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Horvath,M.Ito: "Decidable and undecidable problems of primitive words"Journal of Universal Computer Science. 5. 532-541 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.P.Shum,M.Ito,Y.Q.Guo,Y.Fong: "Semigroups (Editing Book)"Springer. 370 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] C.Nehaniv,M.Ito: "Algebraic Engineering (Editing Book)"World Scientific. 554 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] P.Domosi and M.Ito: "Characterization of languages by lengths of their subwords"Semigroups (edited by K.P.Shum et al.), Monograph Series Springer, Singapore. 117-129 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Ito and P.V.Silva: "Remarks on deletions, scattered deletions and related operations on languages"Semigroups and Application (edited by J.M.Howie et al.) World Scientific, Singapore. 97-105 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] B.Imreh and M.Ito: "A note on the star-product"Acta Cybernetica. 14. 99-104 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Ito: "Shuffle products and related operations on languages"Algebraic Engineering (edited by C.Nehaniv and M.Ito) World Scientific, Singapore. 484-493 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Z.Esik, M.Ito and M.Katsura: "The equational theory of reversal"Algebraic Engineering (edited by C.Nehaniv and M.Ito) World Scientific, Singapore. 502-521 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] B.Imreh and M.Ito: "On some special classes of regular languages"in "Jewels are Forever" (edited by J.Karhumaki, H.Maurer, Gh.Paun & G.Rozenberg) Springer, New York. 25-34 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Horvath and M.Ito: "Decidable and undecidable problems of primitive words"regular and context-free languages, Journal of Universal Computer Science. 5. 532-541 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Ito, L.Kari and G.Thierrin: "Shuffle and scattered deletion closure of languages"Theoretical Computer Science. 245. 115-134 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] B.Imreh, M.Ito and A.Pukler: "On commutative asynchronous automata"Acta Cybernetica. 14. 607-618 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] P.Domosi and M.Ito: "Multiple keyword patterns in context-free languages"in Gh.Paun Festscrift Volume (edited by C.Martin-Vide et al.) (Editura Academiei Romane, Bucuresti). (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] B.Imreh, M.Ito and M.Steinby: "On commutative directable nondeterministic automata"in Gh.Paun Festscrift Volume (edited by C.Martin-Vide et al.) (Editura Academiei Romane, Bucuresti). (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] B.Imreh and M.Ito: "On regular languages determined by nondeterministic directable automata"Theoretical Informatics and Applications. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Ito, C.Martin-Vide and V.Mitrana: "Group weighted finite transducers"Theoretical Informatics and Applications. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Ito, C.Martin-Vide and Gh.Paun: "A characterization of Parikh sets of ETOL languages in terms of P systems"in "Words, Semigroups, and Transductions" (edited by M.Ito et al.) World Scientific. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2002-03-26  

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