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Modular properties of constructor-sharing conditional term rewriting systems

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Conditional and Typed Rewriting Systems (CTRS 1994)

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Abstract

First, using a recent modularity result [Ohl94b] for unconditional term rewriting systems (TRSs), it is shown that semi-completeness is a modular property of constructor-sharing join conditional term rewriting systems (CTRSs). Second, we do not only extend results of Middeldorp [Mid93] on the modularity of termination for disjoint CTRSs to constructor-sharing systems but also simplify the proofs considerably. Moreover, we refute a conjecture of Middeldorp [Mid93] which is related to the aforementioned results.

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References

  1. N. Dershowitz. Hierarchical Termination. 1995. This volume.

    Google Scholar 

  2. N. Dershowitz and J.-P. Jouannaud. Rewrite Systems. In L. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B, chapter 6. North-Holland, 1990.

    Google Scholar 

  3. N. Dershowitz and Z. Manna. Proving Termination with Multiset Orderings. Communications of the ACM 22(8), pages 465–476, 1979.

    Article  Google Scholar 

  4. N. Dershowitz, M. Okada, and G. Sivakumar. Canonical Conditional Rewrite Systems. In Proceedings of the 9th Conference on Automated Deduction, pages 538–549. Lecture Notes in Computer Science 310, Springer Verlag, 1988.

    Google Scholar 

  5. M. Fernández and J.-P. Jouannaud. Modular Termination of Term Rewriting Systems Revisited. In ADT Workshop, 1994.

    Google Scholar 

  6. B. Gramlich. Sufficient Conditions for Modular Termination of Conditional Term Rewriting Systems. In Proceedings of the 3rd International Workshop on Conditional Term Rewriting Systems 1992, pages 128–142. Lecture Notes in Computer Science 656, Springer Verlag, 1993.

    Google Scholar 

  7. B. Gramlich. Abstract Relations between Restricted Termination and Confluence Properties of Rewrite Systems. Fundamenta Informaticae, 1994. To appear.

    Google Scholar 

  8. B. Gramlich. Generalized Sufficient Conditions for Modular Termination of Rewriting. Applicable Algebra in Engineering, Communication and Computing 5, pages 131–158, 1994.

    Google Scholar 

  9. J.W. Klop. Term Rewriting Systems. In S. Abramsky, D. Gabbay, and T. Maibaum, editors, Handbook of Logic in Computer Science, volume 2, pages 1–116. Oxford University Press, 1992.

    Google Scholar 

  10. M. Kurihara and A. Ohuchi. Modular Term Rewriting Systems with Shared Constructors. Journal of Information Processing 14(3), IPS of Japan, pages 357–358, 1991.

    MathSciNet  Google Scholar 

  11. M. Kurihara and A. Ohuchi. Modularity of Simple Termination of Term Rewriting Systems with Shared Constructors. Theoretical Computer Science 103, pages 273–282, 1992.

    Article  Google Scholar 

  12. M. Kurihara and A. Ohuchi. Termination of Combination of Composable Term Rewriting Systems. In Proceedings of the 7th Australian Joint Conference on Artificial Intelligence, 1994. To appear.

    Google Scholar 

  13. M.R.K. Krishna Rao. Completeness of Hierarchical Combinations of Term Rewriting Systems. In Proceedings of the 13th Conference on the Foundations of Software Technology and Theoretical Computer Science, pages 125–139. Lecture Notes in Computer Science 761, Springer Verlag, 1993.

    Google Scholar 

  14. M.R.K. Krishna Rao. Simple Termination of Hierarchical Combinations of Term Rewriting Systems. In Proceedings of the International Symposium on Theoretical Aspects of Computer Software, pages 203–223. Lecture Notes in Computer Science 789, Springer Verlag, 1994.

    Google Scholar 

  15. M. Marchiori. Modularity of Completeness Revisited. In Proceedings of the 6th International Conference on Rewriting Techniques and Applications. Lecture Notes in Computer Science, Springer Verlag, 1995. To appear.

    Google Scholar 

  16. A. Middeldorp. A Sufficient Condition for the Termination of the Direct Sum of Term Rewriting Systems. In Proceedings of the 4th IEEE Symposium on Logic in Computer Science, pages 396–401, 1989.

    Google Scholar 

  17. A. Middeldorp. Modular Properties of Term Rewriting Systems. PhD thesis, Vrije Universiteit te Amsterdam, 1990.

    Google Scholar 

  18. A. Middeldorp. Modular Properties of Conditional Term Rewriting Systems. Information and Computation 104(1), pages 110–158, 1993.

    Article  Google Scholar 

  19. A. Middeldorp. Completeness of Combinations of Conditional Constructor Systems. Journal of Symbolic Computation 17, pages 3–21, 1994.

    Article  Google Scholar 

  20. A. Middeldorp and Y. Toyama. Completeness of Combinations of Constructor Systems. Journal of Symbolic Computation 15(3), pages 331–348, 1993.

    Article  Google Scholar 

  21. E. Ohlebusch. Combinations of Simplifying Conditional Term Rewriting Systems. In Proceedings of the 3rd International Workshop on Conditional Term Rewriting Systems 1992, pages 113–127. Lecture Notes in Computer Science 656, Springer Verlag, 1993.

    Google Scholar 

  22. E. Ohlebusch. Modular Properties of Composable Term Rewriting Systems. PhD thesis, Universität Bielefeld, 1994.

    Google Scholar 

  23. E. Ohlebusch. On the Modularity of Confluence of Constructor-Sharing Term Rewriting Systems. In Proceedings of the 19th Colloquium on Trees in Algebra and Programming, pages 261–275. Lecture Notes in Computer Science 787, Springer Verlag, 1994.

    Google Scholar 

  24. E. Ohlebusch. On the Modularity of Termination of Term Rewriting Systems. Theoretical Computer Science 136, pages 333–360, 1994.

    Article  Google Scholar 

  25. M. Rusinowitch. On Termination of the Direct Sum of Term Rewriting Systems. Information Processing Letters 26, pages 65–70, 1987.

    Article  Google Scholar 

  26. Y. Toyama, J.W. Klop, and H.P. Barendregt. Termination for the Direct Sum of Left-Linear Term Rewriting Systems. In Proceedings of the 3rd International Conference on Rewriting Techniques and Applications, pages 477–491. Lecture Notes in Computer Science 355, Springer Verlag, 1989.

    Google Scholar 

  27. Y. Toyama. Counterexamples to Termination for the Direct Sum of Term Rewriting Systems. Information Processing Letters 25, pages 141–143, 1987.

    Article  Google Scholar 

  28. Y. Toyama. On the Church-Rosser Property for the Direct Sum of Term Rewriting Systems. Journal of the ACM 34(1), pages 128–143, 1987.

    Article  Google Scholar 

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Nachum Dershowitz Naomi Lindenstrauss

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© 1995 Springer-Verlag Berlin Heidelberg

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Ohlebusch, E. (1995). Modular properties of constructor-sharing conditional term rewriting systems. In: Dershowitz, N., Lindenstrauss, N. (eds) Conditional and Typed Rewriting Systems. CTRS 1994. Lecture Notes in Computer Science, vol 968. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60381-6_18

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  • DOI: https://doi.org/10.1007/3-540-60381-6_18

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