Skip to main content
SpringerLink
Log in

The theory of vaccines

  • Session 16: Rewriting
  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1256))

Included in the following conference series:

Abstract

Despite the major role that modularity occupies in computer science, all the known results on modular analysis only treat particular problems, and there is no general unifying theory. In this paper we provide such a general theory of modularity. First, we study the space of the criteria for modularity (the so-called modularity space), and give results on its complexity. Then, we introduce the notion of vaccine and show how it can be used to completely analyze the modular space. It is also shown how vaccines can be effectively used to solve a variety of other modularity problems, providing the best solutions. As an application, we successfully apply the theory to the study of modularity for term rewriting, giving for the first time optimality results, and show how modularity problems can be completely solved.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. F. Barbanera, M. Fernandez, and H. Geuvers. Modularity of strong normalization and confluence in the algebraic A-cube. In Proceedings Nineth IEEE Symposium on Logic in Computer Science, pages 406–415, 1994.

    Google Scholar 

  2. A. Brogi, P. Mancarella, D. Pedreschi, and F. Turini. Modular logic programming. ACM TOPLAS, 16(4), 1994.

    Google Scholar 

  3. N. Dershowitz and J.-P. Jouannaud. Rewrite systems. In J. van Leeuwen, editor, Hand-book of Theoretical Computer Science, volume B, chapter 6, pages 243–320. Elsevier-MIT Press, 1990.

    Google Scholar 

  4. B. Grämlich. Sufficient conditions for modular termination of conditional term rewriting systems. In 3rd Workshop on Conditional Term Rewriting Systems, vol. 656 of LNCS, pp. 128–142. Springer-Verlag, 1993.

    Google Scholar 

  5. B. Grämlich. Generalized sufficient conditions for modular termination of rewriting. Applicable Algebra in Engineering, Communication and Computing, 5:131–158, 1994.

    Google Scholar 

  6. J.-P. Jouannaud and M. Okada. Executable higher-order algebraic specification languages. In Proc. Sixth IEEE Symposium on Logic in Computer Science, pp. 350–361, 1991.

    Google Scholar 

  7. J.W. Klop. Term rewriting systems. In S. Abramsky, Dov M. Gabbay, and T.S.E. Maibaum, editors, Handbook of Logic in Computer Science, volume 2, chapter 1, pages 1–116. Clarendon Press, Oxford, 1992.

    Google Scholar 

  8. M. Kurihara and A. Ohuchi. Modularity of simple termination of term rewriting systems. Journal of IPS Japan, 31(5):633–642, 1990.

    Google Scholar 

  9. M. Marchiori. Modularity of completeness revisited. In J. Hsiang, editor, Proceedings of the Sixth International Conference on Rewriting Techniques and Applications, volume 914 of LNCS, pages 2–10. Springer-Verlag, 1995.

    Google Scholar 

  10. M. Marchiori. The theory of vaccines. Technical Report 27, Dept. of Pure and Applied Mathematics, University of Padova, 1995.

    Google Scholar 

  11. M. Marchiori. Unravelings and ultra-properties. In Proceedings of the Fifth International Conference on Algebraic and Logic Programming (ALP'96), volume 1139 of LNCS, pages 107–121. Springer-Verlag, 1996.

    Google Scholar 

  12. M. Marchiori. Local Analysis and Localizations. PhD thesis, Dept. of Pure and Applied Mathematics, University of Padova, February 1997. In Italian.

    Google Scholar 

  13. A. Middeldorp. A sufficient condition for the termination of the direct sum of term rewriting systems. In Proc. Fourth IEEE Symposium on Logic in Computer Science, pp. 396–401, 1989.

    Google Scholar 

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

    Google Scholar 

  15. E. Ohlebusch. On the modularity of termination of term rewriting systems. Theoretical Computer Science, 136(2):333–360, 1994.

    Article  Google Scholar 

  16. E. Ohlebusch. Modular properties of composable term rewriting systems. Journal of Symbolic Computation, 20(1):1–41, 1995.

    Article  Google Scholar 

  17. M. Rusinowitch. On termination of the direct sum of term rewriting systems. Information Processing Letters, 26:65–70, 1987.

    Article  Google Scholar 

  18. M. Schmidt-Schauß, M. Marchiori, and S.E. Panitz. Modular termination of r-consistent and left-linear term rewriting systems. Theoretical Computer Science, 149(2):361–374, 1995.

    Article  Google Scholar 

  19. Y. Toyama. On the Church-Rosser property for the direct sum of term rewriting systems. Journal of the ACM, 1(34):128–143, 1987.

    Article  Google Scholar 

  20. Y. Toyama, J.W. Klop, and H.P. Barendregt. Termination for direct sums of left-linear complete term rewriting systems. Journal of the ACM, 42(6):1275–1304, November 1995.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Pure and Applied Mathematics, University of Padova, Via Belzoni 7, 35131, Padova, Italy

    Massimo Marchiori

Authors
  1. Massimo Marchiori
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Pierpaolo Degano Roberto Gorrieri Alberto Marchetti-Spaccamela

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Marchiori, M. (1997). The theory of vaccines. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds) Automata, Languages and Programming. ICALP 1997. Lecture Notes in Computer Science, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63165-8_220

Download citation

  • DOI: https://doi.org/10.1007/3-540-63165-8_220

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63165-1

  • Online ISBN: 978-3-540-69194-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation