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A Verification Technique Using Term Rewriting Systems and Abstract Interpretation

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Rewriting Techniques and Applications (RTA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3091))

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Abstract

Verifying the safety property of a transition system given by a term rewriting system is an undecidable problem. In this paper, we give an abstraction for the problem which is automatically generated from a given TRS by using abstract interpretation. Then we show that there are some cases in which the problem can be decided. Also we show a new decidable subclass of term rewriting systems which effectively preserves recognizability.

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References

  1. Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  2. Comon, H.: Equational Formulas in Order-Sorted Algebras. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 674–688. Springer, Heidelberg (1990)

    Chapter  Google Scholar 

  3. Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree Automata Techniques and Applications (1997), http://www.grappa.univ-lille3.fr/tata/

  4. Cousot, P., Cousot, R.: Abstract Interpretation: a Unified Lattice Model for Static Analysis of Programs by Construction or Approximation of Fixpoints. In: Proc. of 4th POPL, pp. 238–252. ACM Press, New York (1977)

    Google Scholar 

  5. Genet, T., Klay, F.: Rewriting for Cryptographic Protocol Verification. In: McAllester, D. (ed.) CADE 2000. LNCS (LNAI), vol. 1831, pp. 271–290. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  6. Gyenizse, P., Vágvölgyi, S.: Linear Generalized Semi-Monadic Rewrite Systems Effectively Preserve Recognizability. Theoretical Computer Science 194(1–2), 87–122 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  7. Meseguer, J., Palomino, M., Martí-Oliet, N.: Equational Abstractions. In: Baader, F. (ed.) CADE 2003. LNCS (LNAI), vol. 2741, pp. 2–16. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  8. Monniaux, D.: Abstracting Cryptographic Protocols with Tree Automata. In: Cortesi, A., Filé, G. (eds.) SAS 1999. LNCS, vol. 1694, pp. 149–163. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  9. Nielson, F., Nielson, H.R., Hankin, C.: Abstract Interpretation. In: Principles of Program Analysis, ch. 4, Springer, Heidelberg (1999)

    Google Scholar 

  10. Salomaa, K.: Decidability of Confluence and Termination of Monadic Term Rewriting Systems. In: Book, R.V. (ed.) RTA 1991. LNCS, vol. 488, pp. 275–286. Springer, Heidelberg (1991)

    Google Scholar 

  11. Takai, T., Kaji, Y., Seki, H.: Right-linear Finite Path Overlapping Term Rewriting Systems Effectively Preserve Recognizability. In: Bachmair, L. (ed.) RTA 2000. LNCS, vol. 1833, pp. 246–260. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  12. Takai, T., Kaji, Y., Seki, H.: Right-linear Finite-Path Overlapping Term Rewriting Systems Effectively Preserve Recognizability. Scienticae Mathematicae Japonicae (to appear)

    Google Scholar 

  13. Takai, T., Seki, H., Fujinaka, Y., Kaji, Y.: Layered Transducing Term Rewriting System and Its Recognizability Preserving Property. IEICE Transactions on Information and Systems E86-D(2), 285–295 (2003)

    Google Scholar 

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Takai, T. (2004). A Verification Technique Using Term Rewriting Systems and Abstract Interpretation. In: van Oostrom, V. (eds) Rewriting Techniques and Applications. RTA 2004. Lecture Notes in Computer Science, vol 3091. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25979-4_9

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  • DOI: https://doi.org/10.1007/978-3-540-25979-4_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22153-1

  • Online ISBN: 978-3-540-25979-4

  • eBook Packages: Springer Book Archive

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