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Deciding WQO for Factorial Languages

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7810))

Abstract

A language is factorial if it is closed under taking factors (i.e. contiguous subwords). Every factorial language can be described by an antidictionary, i.e. a minimal set of forbidden factors. We show that the problem of deciding whether a factorial language given by a finite antidictionary is well-quasi-ordered under the factor containment relation can be solved in polynomial time.

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References

  1. Atkinson, M.D., Murphy, M.M., Ruškuc, M.: Partially well-ordered closed sets of permutations. Order 19(2), 101–113 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Brignall, R., Ruškuc, N., Vatter, V.: Simple permutations: decidability and unavoidable substructures. Theoretical Computer Science 391(1-2), 150–163 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cherlin, G.L., Latka, B.J.: Minimal antichains in well-founded quasi-orders with an application to tournaments. J. Comb. Theory, Ser. B 80(2), 258–276 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  4. Crochemore, M., Mignosi, F., Restivo, A.: Automata and forbidden words. Inf. Process. Lett. 67(3), 111–117 (1998)

    Article  MathSciNet  Google Scholar 

  5. Ding, G.: Subgraphs and well-quasi-ordering. J. Graph Theory 16(5), 489–502 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  6. Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! Theor. Comput. Sci. 256(1-2), 63–92 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hine, N., Oxley, J.: When excluding one matroid prevents infinite antichains. Advances in Applied Mathematics 45(1), 74–76 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Korpelainen, N., Lozin, V.V.: Two forbidden induced subgraphs and well-quasi-ordering. Discrete Mathematics 311(6), 1813–1822 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kruskal, J.B.: The theory of well-quasi-ordering: a frequently discovered concept. J. Comb. Theory, Ser. A 13(3), 297–305 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  10. de Luca, A., Varricchio, S.: Well quasi-orders and regular languages. Acta Inf. 31(6), 539–557 (1994)

    Article  Google Scholar 

  11. Robertson, N., Seymour, P.: Graph Minors. XX. Wagner’s conjecture. J. Comb. Theory, Ser. B 92(2), 325–357 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. Spielman, D.A., Bóna, M.: An infinite antichain of permutations. The Electr. J. Comb. 7 (2000)

    Google Scholar 

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© 2013 Springer-Verlag Berlin Heidelberg

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Atminas, A., Lozin, V., Moshkov, M. (2013). Deciding WQO for Factorial Languages. In: Dediu, AH., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2013. Lecture Notes in Computer Science, vol 7810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37064-9_8

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  • DOI: https://doi.org/10.1007/978-3-642-37064-9_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37063-2

  • Online ISBN: 978-3-642-37064-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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