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On the word problem for free lattices

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Rewriting Techniques and Applications (RTA 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1232))

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Abstract

We prove completeness of a rewrite-based algorithm for the word problem in the variety of lattices and discuss the method of non-symmetric completion with regard to this variety.

I wish to thank Harald Ganzinger, Jürgen Stuber and the anonymous referees for helpful comments.

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References

  1. L. Bachmair and D. Plaisted. Termination orderings for associative-commutative rewriting systems. J. Symbolic Computation, 1(4):329–349, 1985.

    Google Scholar 

  2. C. Delor and L. Puel. Extension of the associative path ordering to a chain of associative-commutative symbols. In C. Kirchner, editor, Rewriting Techniques and Applications, volume 690 of LNCS, pages 389–404. Springer-Verlag, 1993.

    Google Scholar 

  3. R. Freese, J. Ječek, and J.B. Nation. Term rewrite systems for lattice theory. J. Symbolic Computation, 16:279–288, 1993.

    Google Scholar 

  4. R. Freese, J. Ječek, and J.B. Nation. Free Lattices, volume 42 of Surveys and Monographs. American Mathematical Society, 1995.

    Google Scholar 

  5. J. Levy and J. Agustí. Bi-rewriting, a term rewriting technique for monotonic order relations. In C. Kirchner, editor, Rewriting Techniques and Applications, volume 690 of LNCS, pages 17–31. Springer-Verlag, 1993.

    Google Scholar 

  6. J. Levy and J. Agustí. Bi-rewrite systems. J. Symbolic Computation, 22:279–314, 1996.

    Google Scholar 

  7. R.N. McKenzie, G.F. McNulty, and W.F. Taylor. Algebras, Varieties and Lattices, volume I. Wadsworth & Brooks/Cole, 1987.

    Google Scholar 

  8. G. Struth. Non-symmetric rewriting. Technical Report MPI-I-96-2-004, Max-Planck-Institut für Informatik, Saarbrücken, 1996.

    Google Scholar 

  9. Ph.M. Whitman. Free lattices. Ann. of Math., 42(2):325–330, 1941.

    Google Scholar 

  10. Ph.M. Whitman. Free lattices (II). Ann. of Math., 43(2):104–115, 1942.

    Google Scholar 

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Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Im Stadtwald, D-66123, Saarbrücken, Germany

    Georg Struth

Authors
  1. Georg Struth
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Hubert Comon

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© 1997 Springer-Verlag Berlin Heidelberg

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Struth, G. (1997). On the word problem for free lattices. In: Comon, H. (eds) Rewriting Techniques and Applications. RTA 1997. Lecture Notes in Computer Science, vol 1232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62950-5_66

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  • DOI: https://doi.org/10.1007/3-540-62950-5_66

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62950-4

  • Online ISBN: 978-3-540-69051-1

  • eBook Packages: Springer Book Archive

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