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Large Simple Binary Equality Words

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Developments in Language Theory (DLT 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5257))

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Abstract

Let w be an equality word of two nonperiodic binary morphisms g,h:{a,b}*→Δ *. Suppose that no overflow occurs twice in w and that w contains at least 9 occurrences of a and at least 9 occurrences of b.

Then either w = (ab)i a, or w = a i b j with \(\gcd(i,j)=1\), up to the exchange of letters a and b.

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References

  1. Salomaa, A.: Equality sets for homomorphisms of free monoid. Acta Cybern. 4, 127–139 (1980)

    MathSciNet  Google Scholar 

  2. Čulík II, K.: A purely homomorphic characterization of recursively enumerable sets. J. ACM 26(2), 345–350 (1979)

    Article  MATH  Google Scholar 

  3. Post, E.: A variant of a recursively unsolvable problem. Bulletin of the American Mathematical Society 52, 264–268 (1946)

    Article  MATH  MathSciNet  Google Scholar 

  4. Karhumäki, J.: On recent trends in formal language theory. In: Ottmann, T. (ed.) ICALP 1987. LNCS, vol. 267, pp. 136–162. Springer, Heidelberg (1987)

    Google Scholar 

  5. Karhumäki, J.: Open problems and exercises on words and languages (invited talk). In: Proceedings of Conference on Algebraic Information, Aristotle University of Thessaloniki, pp. 295–305 (2005)

    Google Scholar 

  6. Čulík, I.K., Karhumäki, J.: On the equality sets for homomorphisms on free monoids with two generators. ITA 14(4), 349–369 (1980)

    MATH  Google Scholar 

  7. Ehrenfeucht, A., Karhumäki, J., Rozenberg, G.: On binary equality sets and a solution to the test set conjecture in the binary case. J. Algebra 85(1), 76–85 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  8. Holub, Š.: Binary equality sets are generated by two words. Journal of Algebra 259, 1–42 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Holub, Š.: A unique structure of two-generated binary equality sets. In: Developments in Language Theory, pp. 245–257 (2002)

    Google Scholar 

  10. Holub, Š.: Binary equality languages for periodic morphisms. In: Huang, C.-H., Sadayappan, P., Sehr, D. (eds.) LCPC 1997. LNCS, vol. 1366, pp. 52–54. Springer, Heidelberg (1998)

    Google Scholar 

  11. Maňuch, J.: Defect effect of bi-infinite words in the two-element case. Discrete Mathematics and Theoretical Computer Science 4(2), 273–290 (2001)

    MATH  MathSciNet  Google Scholar 

  12. Ehrenfeucht, A., Karhumäki, J., Rozenberg, G.: The (generalized) Post Correspondence Problem with lists consisting of two words is decidable. Theor. Comput. Sci. 21, 119–144 (1982)

    Article  MATH  Google Scholar 

  13. Halava, V., Holub, Š.: Binary (generalized) Post Correspondence Problem is in P. Technical Report 785, TUCS (September 2006)

    Google Scholar 

  14. Lothaire, M.: Combinatorics on words. Addison-Wesley, Reading (1983)

    MATH  Google Scholar 

  15. Rozenberg, G., Salomaa, A. (eds.): Handbook of formal languages. word, language, grammar, vol. 1. Springer, New York (1997)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University, 186 75 Praha 8, Sokolovská 83, Czech Republic

    Jana Hadravová & Štěpán Holub

Authors
  1. Jana Hadravová
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  2. Štěpán Holub
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Masami Ito Masafumi Toyama

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© 2008 Springer-Verlag Berlin Heidelberg

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Hadravová, J., Holub, Š. (2008). Large Simple Binary Equality Words. In: Ito, M., Toyama, M. (eds) Developments in Language Theory. DLT 2008. Lecture Notes in Computer Science, vol 5257. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85780-8_31

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  • DOI: https://doi.org/10.1007/978-3-540-85780-8_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85779-2

  • Online ISBN: 978-3-540-85780-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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