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Simple termination of hierarchical combinations of term rewriting systems

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Theoretical Aspects of Computer Software (TACS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 789))

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Abstract

In this paper, we study modular aspects of hierarchical combinations of term rewriting systems. A class of hierarchical combinations is identified for which simple termination is modular. Our result generalizes Kurihara and Ohuchi's result on modularity of simple termination of rewrite systems with shared constructors. The result is extended to conditional term rewriting systems generalizing Ohlebusch's result.

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References

  1. N. Dershowitz and J.-P. Jouannaud (1990), Rewrite Systems, In J. van Leeuwen (ed.), Handbook of Theoretical Computer Science, Vol. B, pp. 243–320, North-Holland.

    Google Scholar 

  2. N. Dershowitz (1992), Hierarchical termination, draft, Hebrew University, Jerusalem 91904, Israel, December 1992.

    Google Scholar 

  3. K. Drosten (1989), termersetzungssysteme, Informatik-Fachberichte Vol. 210, Springer.

    Google Scholar 

  4. B. Gramlich (1992), Relating innermost, weak, uniform and modular termination of term rewrite systems, Proc. of Logic Prog. and Automated Reasoning, LPAR'92, Lecture Notes in Computer Science 624, pp. 285–296, Springer-Verlag.

    Google Scholar 

  5. B.Grämlich (1991), A structural analysis of modular termination of term rewriting systems, to appear in Applicable algebra in Engineering, Communication and Computing.

    Google Scholar 

  6. G. Huet and D.C. Oppen (1980), Equations and rewrite rules: A survey, in R.V. Book (ed.) Formal Languages, Perspectives and Open Problems, pp. 349–405.

    Google Scholar 

  7. J.W. Klop (1992), Term Rewriting Systems, tech rep. CS-R9073, CWI, Amsterdam. Also appears as a chapter in S. Abramsky, D. Gabby and T. Maibaum (ed.), Handbook of Logic in Computer Science, Vol. 1, Oxford Press, 1992.

    Google Scholar 

  8. M.R.K. Krishna Rao, D. Kapur and R.K. Shyamasundar (1991), A Transformational methodology for proving termination of logic programs, Proc. of Computer Science Logic, CSL'91, Lecture Notes in Computer Science 626, pp. 213–226, Springer-Verlag.

    Google Scholar 

  9. M.R.K. Krishna Rao (1992), modular proofs for completeness of hierarchical systems, technical report, TIFR, Bombay, December 1992.

    Google Scholar 

  10. M.R.K. Krishna Rao (1993), Completeness of hierarchical combinations of term rewriting systems, Proc. of 13th conference on Foundations of Software Technology and Theoretical Computer Science, FST&TCS'93, Lecture Notes in Computer Science 761, pp. 125–139, Springer-Verlag.

    Google Scholar 

  11. M. Kurihara and A. Ohuchi (1990). Modularity of simple termination of term rewriting systems, Journal of IPS, Japan 34, pp. 632–642.

    Google Scholar 

  12. M. Kurihara and A. Ohuchi (1992), Modularity of simple termination of term rewriting systems with shared constructors, Theoretical Computer Science 103, pp. 273–282.

    Google Scholar 

  13. A. Middeldorp (1989), A sufficient condition for the termination of the direct sum of term rewriting systems, Proc. of LICS'89, pp. 396–401.

    Google Scholar 

  14. A. Middeldorp (1990), Modular properties of term rewriting systems, Ph.D. Thesis, Free University, Amsterdam.

    Google Scholar 

  15. A. Middeldorp and Y. Toyama (1991), Completeness of combinations of constructor systems, Proc. of RTA'91, Lecture Notes in Computer Science 488, pp. 188–199, Springer-Verlag. Also appears in J. Symb. Comp. 15, pp. 331–348.

    Google Scholar 

  16. A. Middeldorp and B. Gramlich (1993), Simple termination is difficult, Proc. RTA'93, Lecture Notes in Computer Science 690, pp. 228–242, Springer-Verlag.

    Google Scholar 

  17. E. Ohlebusch (1992), A note on simple termination of infinite term rewriting systems, Report no. 7, Univ. of Bielefeld.

    Google Scholar 

  18. E. Ohlebusch (1992), Combinations of simplifying conditional term rewriting systems, Proc. CTRS'92, Lecture Notes in Computer Science 656, pp. 113–127, Springer-Verlag.

    Google Scholar 

  19. E. Ohlebusch (1993), A simple proof of sufficient conditions for the termination of disjoint union of TRSs, Bulletin of EATCS 49, pp. 178–183.

    Google Scholar 

  20. E. Ohlebusch (1993), On the modularity of termination of term rewriting systems, Report no. 11, Univ. of Bielefeld.

    Google Scholar 

  21. M. Rusinowitch (1987), On termination of the direct sum of term rewriting systems, Information Processing Letters, IPL 26, pp. 65–70.

    Google Scholar 

  22. Y. Toyama (1987), On Church-Rosser property for the direct sum of term rewriting systems, JACM 34, pp. 128–143.

    Google Scholar 

  23. Y. Toyama (1987), Counterexamples to termination for the direct sum of term rewriting systems, Information Processing Letters, IPL 25, pp. 141–143.

    Google Scholar 

  24. Y. Toyama, J.W. Klop and H.P. Barendregt (1989), Termination for the direct sum of left-linear term rewriting systems, Proc. of RTA'89, Lecture Notes in Computer Science 355, pp. 477–491, Springer-Verlag.

    Google Scholar 

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Authors and Affiliations

  1. Computer Science Group, Tata Institute of Fundamental Research, 400 005, Colaba, Bombay, India

    M. R. K. Krishna Rao

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  1. M. R. K. Krishna Rao
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Masami Hagiya John C. Mitchell

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© 1994 Springer-Verlag Berlin Heidelberg

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Rao, M.R.K.K. (1994). Simple termination of hierarchical combinations of term rewriting systems. In: Hagiya, M., Mitchell, J.C. (eds) Theoretical Aspects of Computer Software. TACS 1994. Lecture Notes in Computer Science, vol 789. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57887-0_97

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  • DOI: https://doi.org/10.1007/3-540-57887-0_97

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57887-1

  • Online ISBN: 978-3-540-48383-0

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