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On Classes of Regular Languages Related to Monotone WQOs

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Book cover Descriptional Complexity of Formal Systems (DCFS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11612))

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Abstract

We study relationships of monotone well quasiorders to regular languages and \(\omega \)-languages, concentrating on decidability of the lattices of upper sets on words and infinite words. We establish rather general sufficient conditions for decidability. Applying these conditions to concrete natural monotone WQOs, we obtain new decidability results and new proofs of some known results.

M. Ogawa—This research was partially supported by Japan Society for the Promotion of Science (JSPS), Core-to-Core Program (A. Advanced Research Networks).

V. Selivanov—The research of V. Selivanov was supported by Russian Science Foundation, project 18-11-00100.

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References

  1. Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge (1994)

    Google Scholar 

  2. Ehrenfeucht, A., Haussler, D., Rozenberg, G.: On regularity of context-free languages. Theor. Comput. Sci. 27, 311–332 (1983)

    Article  MathSciNet  Google Scholar 

  3. Glaßer, C., Schmitz, H.: The boolean structure of dot-depth one. J. Autom. Lang. Comb. 6(4), 437–452 (2001). https://doi.org/10.25596/jalc-2001-437

    Article  MathSciNet  MATH  Google Scholar 

  4. Glaßer, C., Schmitz, H., Selivanov, V.L.: Efficient algorithms for membership in boolean hierarchies of regular languages. Theor. Comput. Sci. 646(C), 86–108 (2016). https://doi.org/10.1016/j.tcs.2016.07.017

    Article  MathSciNet  MATH  Google Scholar 

  5. Higman, G.: Ordering by divisibility in abstract algebras. Proc. Lond. Math. Soc. s3–2(1), 326–336 (1952). https://doi.org/10.1112/plms/s3-2.1.326

    Article  MathSciNet  MATH  Google Scholar 

  6. Kříž, I., Thomas, R.: Ordinal types in ramsey theory and well-partial-ordering theory. In: Neše tř il, J., Rödl, V. (eds.) Mathematics of Ramsey Theory. Algorithms and Combinatorics, vol. 5. Springer, Heidelberg (1990). https://doi.org/10.1007/978-3-642-72905-8_7

    Chapter  Google Scholar 

  7. Laver, R.: Better-quasi-orderings and a class of trees. In: Studies in foundations and combinatorics, Advances in mathematics: Supplementary studies, vol. 1, pp. 31–48. Academic Press (1978)

    Google Scholar 

  8. de Luca, A., Varricchio, S.: Finiteness and Regularity in Semigroups and Formal Languages. Monographs in Theoretical Computer Science. Springer, Heidelberg (1999). https://doi.org/10.1007/978-3-642-59849-4

    Book  MATH  Google Scholar 

  9. Marcone, A.: Foundations of BQO theory. Trans. AMS 345(2), 641–660 (1994)

    Article  MathSciNet  Google Scholar 

  10. Marcone, A.: Fine analysis of the quasi-orderings on the power set. Order 18(4), 339–347 (2001). https://doi.org/10.1023/A:1013952225669

    Article  MathSciNet  MATH  Google Scholar 

  11. Nash-Williams, C.S.J.A.: On well-quasi-ordering transfinite sequences. Math. Proc. Cambridge Philos. Soc. 61, 33–39 (1965)

    Article  MathSciNet  Google Scholar 

  12. Ogawa, M.: Well-quasi-orders and regular omega-languages. Theor. Comput. Sci. 324(1), 55–60 (2004). https://doi.org/10.1016/j.tcs.2004.03.052

    Article  MATH  Google Scholar 

  13. Perrin, D., Pin, J.: Infinite Words, Pure and Applied Mathematics, vol. 141 (2004)

    Google Scholar 

  14. Pin, J.: Positive varieties and infinite words. In: Lucchesi, C.L., Moura, A.V. (eds.) LATIN 1998. LNCS, vol. 1380, pp. 76–87. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0054312

    Chapter  Google Scholar 

  15. Rado, R.: Partial well-ordering of sets of vectors. Mathematika 1, 89–95 (1954)

    Article  MathSciNet  Google Scholar 

  16. Rogers Jr., H.: Theory of recursive functions and effective computability. McGraw-Hill, New York (1967)

    MATH  Google Scholar 

  17. Selivanov, V.L.: A logical approach to decidability of hierarchies of regular star—free languages. In: Ferreira, A., Reichel, H. (eds.) STACS 2001. LNCS, vol. 2010, pp. 539–550. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44693-1_47

    Chapter  Google Scholar 

  18. Selivanov, V.L.: Hierarchies and reducibilities on regular languages related to modulo counting. RAIRO Theor. Inform. Appl. 43(1), 95–132 (2009)

    Article  MathSciNet  Google Scholar 

  19. Thomas, W.: Automata on infinite objects. In: Handbook of Theoretical Computer Science, vol. B, pp. 133–192. Elsevier Science Publishers (1990)

    Google Scholar 

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Authors and Affiliations

  1. Japan Advanced Institute of Science and Technology, Nomi, Japan

    Mizuhito Ogawa

  2. A.P. Ershov Institute of Informatics Systems SB RAS, Novosibirsk, Russia

    Victor Selivanov

  3. Kazan Federal University, Kazan, Russia

    Victor Selivanov

Authors
  1. Mizuhito Ogawa
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  2. Victor Selivanov
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Corresponding author

Correspondence to Victor Selivanov .

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Editors and Affiliations

  1. Slovak Academy of Sciences, Košice, Slovakia

    Michal Hospodár

  2. Slovak Academy of Sciences, Košice, Slovakia

    Galina Jirásková

  3. Saint Mary's University, Halifax, NS, Canada

    Stavros Konstantinidis

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Ogawa, M., Selivanov, V. (2019). On Classes of Regular Languages Related to Monotone WQOs. In: Hospodár, M., Jirásková, G., Konstantinidis, S. (eds) Descriptional Complexity of Formal Systems. DCFS 2019. Lecture Notes in Computer Science(), vol 11612. Springer, Cham. https://doi.org/10.1007/978-3-030-23247-4_18

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  • DOI: https://doi.org/10.1007/978-3-030-23247-4_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-23246-7

  • Online ISBN: 978-3-030-23247-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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