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Time bounded rewrite systems and termination proofs by generalized embedding

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Rewriting Techniques and Applications (RTA 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 488))

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Abstract

It is shown that term rewriting systems with primitive recursively bounded derivation heights can be simulated by rewriting systems that have termination proofs using generalized embedding, a very restricted class of simplification orderings. As a corollary we obtain a characterization of the class of relations computable by rewrite systems having primitive recursively bounded derivation heights using recent results on termination proofs by multiset path orderings.

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References

  1. Börger, E. Computability, Complexity, Logic, North Holland (1989).

    Google Scholar 

  2. Cichon, E.A. Bounds on Derivation Lengths from Termination Proofs, Report CSD-TR-622, University of London, Egham (1990). To appear in Proc. Conf. on Proof Theory, Leeds (1990).

    Google Scholar 

  3. Dershowitz, N. Orderings for term rewriting systems, TCS 17 (3) (1982), pp. 279–301.

    Google Scholar 

  4. Dershowitz, N., Jouannaud, J.-P. Rewrite systems, in: Handbook of Theoretical Computer Science, Vol. 2, Ed. J. van Leeuwen, North Holland (1990).

    Google Scholar 

  5. Dershowitz, N., Okada, M. Proof-theoretic techniques for term rewriting theory, Proc. 3rd LICS (1989), pp. 104–111.

    Google Scholar 

  6. Drewes, F., Lautemann, C. Incremental Termination Proofs and the Length of Derivations, Report 7/90, Universität Bremen (1990).

    Google Scholar 

  7. Geser, A. Termination relative, Ph.D. thesis, Univ. Passau (1990).

    Google Scholar 

  8. Hofbauer, D. Termination proofs by multiset path orderings imply primitive recursive derivation lengths, Proc. 2nd ALP, LNCS 463 (1990), pp. 347–358.

    Google Scholar 

  9. Hofbauer, D. Time bounded rewrite systems and termination proofs by generalized embedding, Report, Technische Universität Berlin (1991).

    Google Scholar 

  10. Hofbauer, D., Lautemann, C. Termination proofs and the length of derivations, Proc. 3rd RTA, LNCS 355 (1989), pp. 167–177.

    Google Scholar 

  11. Jouannaud, J.-P., Lescanne, P., Reinig, F. Recursive decomposition ordering, IFIP Working Conf., Ed. Bjørner, North Holland (1982), pp. 331–348.

    Google Scholar 

  12. Klop, J.W. Term rewriting systems: A tutorial, Bulletin of the EATCS 32 (1987), pp. 143–183.

    Google Scholar 

  13. Kapur, D., Narendran, P., Sivakumar, G. A path ordering for proving termination of term rewriting systems, Proc. 10th CAAP, LNCS 185 (1985), pp. 173–187.

    Google Scholar 

  14. Plaisted, D. A recursively defined ordering for proving termination of term rewriting systems, Report UIUCDCS-R-78-943, University of Illinois, Urbana (1978).

    Google Scholar 

  15. Rose, H.E. Subrecursion: Functions and hierarchies, Oxford University Press (1984).

    Google Scholar 

  16. Rusinowitch, M. Path of subterms ordering and recursive decomposition ordering revisited, J. Symbolic Comp. 3 (1&2) (1987), pp. 117–131.

    Google Scholar 

  17. Steinbach, J. Extensions and comparison of simplification orderings, Proc. 3rd RTA, LNCS 355, pp. 434–448.

    Google Scholar 

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Ronald V. Book

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© 1991 Springer-Verlag Berlin Heidelberg

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Hofbauer, D. (1991). Time bounded rewrite systems and termination proofs by generalized embedding. In: Book, R.V. (eds) Rewriting Techniques and Applications. RTA 1991. Lecture Notes in Computer Science, vol 488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53904-2_86

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  • DOI: https://doi.org/10.1007/3-540-53904-2_86

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53904-9

  • Online ISBN: 978-3-540-46383-2

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