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Deciding the Word Problem in the Union of Equational Theories Sharing Constructors

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Rewriting Techniques and Applications (RTA 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1631))

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Abstract

The main contribution of this paper is a new method for combining decision procedures for the word problem in equational the- ories sharing “constructors.” The notion of constructors adopted in this paper has a nice algebraic definition and is more general than a related notion introduced in previous work on the combination problem.

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References

  1. F. Baader and K.U. Schulz. Unification in the union of disjoint equational theories: Combining decision procedures. J. Symbolic Computation 21, 1996.

    Google Scholar 

  2. F. Baader and C. Tinelli. A new approach for combining decision procedures for the word problem, and its connection to the Nelson-Oppen combination method. In Proc. CADE-14, Springer LNAI 1249, 1997.

    Google Scholar 

  3. F. Baader and C. Tinelli. Deciding the word problem in the union of equational theories. UIUCDCS-Report 98-2073, Department of Computer Science, University of Illinois at Urbana-Champaign, 1998. Available at http://www-lti.informatik.rwth-aachen.de/Forschung/Papers.html.

  4. A. Boudet. Combining unification algorithms. J. Symbolic Computation 16, 1993.

    Google Scholar 

  5. N. Dershowitz and Z. Manna. Proving termination with multiset orderings. Communications of the ACM 22, 1979.

    Google Scholar 

  6. E. Domenjoud, F. Klay, and C. Ringeissen. Combination techniques for non-disjoint equational theories. In Proc. CADE-12, Springer LNAI 814, 1994.

    Google Scholar 

  7. H. Kirchner and Ch. Ringeissen. Combining symbolic constraint solvers on algebraic domains. J. Symbolic Computation 18, 1994.

    Google Scholar 

  8. T. Nipkow. Combining matching algorithms: The regular case. In Proc. RTA’89, Springer LNCS 335, 1989.

    Google Scholar 

  9. E. Ohlebusch. Modular properties of composable term rewriting systems. J. Symbolic Computation 20, 1995.

    Google Scholar 

  10. D. Pigozzi. The join of equational theories. Colloquium Mathematicum 30, 1974.

    Google Scholar 

  11. Ch. Ringeissen. Unification in a combination of equational theories with shared constants and its application to primal algebras. In Proc. LPAR’92, Springer LNAI 624, 1992.

    Google Scholar 

  12. Ch. Ringeissen. Combination of matching algorithms. In Proc. STACS-11, Springer LNCS 775, 1994.

    Google Scholar 

  13. M. Schmidt-Schauff. Combination of unification algorithms. J. Symbolic Computation 8, 1989.

    Google Scholar 

  14. E. Tidén. First-Order Unification in Combinations of Equational Theories. Phd thesis, The Royal Institute of Technology, Stockholm, 1986.

    MATH  Google Scholar 

  15. C. Tinelli and Ch. Ringeissen. Non-disjoint unions of theories and combinations of satisàbility procedures: First results. Technical Report UIUCDCS-R-98-2044, Department of Computer Science, University of Illinois at Urbana-Champaign, April 1998. (Also available as INRIA research report no. RR-3402.)

    Google Scholar 

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Author information

Authors and Affiliations

  1. LuFg Theoretical Computer Science, RWTH Aachen, Ahornstraße, 55, 52074, Aachen, Germany

    Franz Baader

  2. Department of Computer Science, University of Illinois at Urbana-Champaign, 1304, W. Springfield Ave, Urbana, IL, 61801, USA

    Cesare Tinelli

Authors
  1. Franz Baader
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  2. Cesare Tinelli
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University at Albany — SUNY, Albany, NY, 12222, USA

    Paliath Narendran

  2. LORIA — INRIA Lorraine 615, rue du Jardin Botanique, F-54602, Villers les Nancy, Cedex, France

    Michael Rusinowitch

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© 1999 Springer-Verlag Berlin Heidelberg

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Baader, F., Tinelli, C. (1999). Deciding the Word Problem in the Union of Equational Theories Sharing Constructors. In: Narendran, P., Rusinowitch, M. (eds) Rewriting Techniques and Applications. RTA 1999. Lecture Notes in Computer Science, vol 1631. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48685-2_14

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  • DOI: https://doi.org/10.1007/3-540-48685-2_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66201-3

  • Online ISBN: 978-3-540-48685-5

  • eBook Packages: Springer Book Archive

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