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A Unique Structure of Two-Generated Binary Equality Sets

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Developments in Language Theory (DLT 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2450))

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Abstract

Let L be the equality set of two distinct injective morphisms g and h, and let L be generated by at least two words. Recently it was proved ([2]) that such an L is generated by two words and g and h can be chosen marked from both sides. We use this result to show that L is of the form {a i b, ba i}*, with i ≥ 1.

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References

  1. A. Ehrenfeucht, J. Karhumäki, and G. Rozenberg, The (generalized) Post correspondence problem with lists consisting of two words is decidable, Theoret. Comput. Sci. 21 (1982), no. 2, 119–144.

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  2. Š. Holub, Binary equality sets are generated by two words, J. Algebra, DOI: 10.1016/S0021-8693(02)00534-3, in press.

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  3. K. Culik II and J. Karhumäki, On the equality sets for homomorphisms on free monoids with two generators, RAIRO Theor. Informatics 14 (1980), 349–369.

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

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© 2003 Springer-Verlag Berlin Heidelberg

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Holub, Š. (2003). A Unique Structure of Two-Generated Binary Equality Sets. In: Ito, M., Toyama, M. (eds) Developments in Language Theory. DLT 2002. Lecture Notes in Computer Science, vol 2450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45005-X_21

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  • DOI: https://doi.org/10.1007/3-540-45005-X_21

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40431-6

  • Online ISBN: 978-3-540-45005-4

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