Skip to main content

Modularity of termination in term graph rewriting

  • Regular Papers
  • Conference paper
  • First Online:
Rewriting Techniques and Applications (RTA 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1103))

Included in the following conference series:

  • 119 Accesses

Abstract

Term rewriting is generally implemented using graph rewriting for efficiency reasons. Graph rewriting allows sharing of common structures thereby saving both time and space. This implementation is sound in the sense that computation of a normal form of a graph yields a normal form of the corresponding term. In this paper, we study modularity of termination of the graph reduction. Unlike in the case of term rewriting, termination is modular in graph rewriting for a large class of systems. Our results generalize the results of Plump [14] and Kurihara and Ohuchi [10].

On leave from Tata Institute of Fundamental Research, Bombay

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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.

    Google Scholar 

  2. N. Dershowitz (1992), Hierarchical termination, draft, Hebrew University, Dec. 1992. Revised version in Proc. CTRS'94, LNCS 968, Springer-Verlag.

    Google Scholar 

  3. M. Fernandez and J.P. Jouannaud (1995), Modular termination of term rewriting systems revisited, Proc. COMPASS workshop on ADT, LNCS 906, pp. 255–273.

    Google Scholar 

  4. B. Gramlich (1994), Generalized sufficient conditions for modular termination of rewriting, in AAECC 5, pp. 131–158.

    Article  Google Scholar 

  5. J.W. Klop (1992), Term Rewriting Systems, in S. Abramsky, D. Gabbay and T. Maibaum (ed.), Handbook of Logic in Computer Science, Vol. 2.

    Google Scholar 

  6. M.R.K. Krishna Rao (1994), Simple termination of hierarchical combinations of term rewriting systems, Proc. of TACS'94, LNCS 789, pp. 203–223.

    Google Scholar 

  7. M.R.K. Krishna Rao (1995), Semi-completeness of hierarchical and superhierarchical combinations of term rewriting systems, Proc. of TAPSOFT'95, LNCS 915, pp. 379–393.

    Google Scholar 

  8. M.R.K. Krishna Rao (1995), Graph reducibility of term rewriting systems, Proc. of MFCS'95, LNCS 969, pp. 371–381.

    Google Scholar 

  9. M.R.K. Krishna Rao (1995), Modular proofs for completeness of hierarchical term rewriting systems, Theoretical Computer Science 151, pp. 487–512.

    Article  Google Scholar 

  10. M. Kurihara and A. Ohuchi (1995), Modularity in noncopying term rewriting, Theoretical Computer Science 152, pp. 139–169.

    Google Scholar 

  11. A. Middeldorp and Y. Toyama (1993), Completeness of combinations of constructor systems, J. Symb. Comp. 15, pp. 331–348.

    Google Scholar 

  12. E. Ohlebusch (1994), Modular properties of composable term rewriting systems, Ph.D. Thesis, University of Bielefeld.

    Google Scholar 

  13. D. Plump (1990), Graph-reducible term rewriting systems, Proc. 4th workshop on graph grammars and their applications to Computer Science, LNCS 532, pp. 622–636.

    Google Scholar 

  14. D. Plump (1992), Collapsed tree rewriting: completeness, confluence and modularity, Proc. CTRS'92, LNCS 656, pp. 97–112.

    Google Scholar 

  15. D. Plump (1993), Evaluation of functional expressions by hypergraph rewriting, Ph.D. Thesis, University of Bremen.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Harald Ganzinger

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Rao, M.R.K.K. (1996). Modularity of termination in term graph rewriting. In: Ganzinger, H. (eds) Rewriting Techniques and Applications. RTA 1996. Lecture Notes in Computer Science, vol 1103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61464-8_55

Download citation

  • DOI: https://doi.org/10.1007/3-540-61464-8_55

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61464-7

  • Online ISBN: 978-3-540-68596-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics