Skip to main content

Over-Approximating Terms Reachable by Context-Sensitive Rewriting

  • Conference paper
  • First Online:
Reachability Problems (RP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9328))

Included in the following conference series:

Abstract

For any left-linear context-sensitive term rewrite system and any regular language of ground terms I, we build a finite tree automaton that recognizes a superset of the descendants of I, i.e. of the terms reachable from I by context-sensitive rewriting.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 44.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andrianarivelo, N., Réty, P.: Over-Approximating Terms Reachable by Context-Sensitive Rewriting (full version). Technical Report RR-2015-02, LIFO, Université d’Orléans (2015)

    Google Scholar 

  2. Boichut, Y., Chabin, J., Réty, P.: Over-approximating descendants by synchronized tree languages. In: Proceedings of the International Conference RTA. LIPIcs, vol. 21, pp. 128–142 (2013)

    Google Scholar 

  3. Boichut, Y., Genet, T., Jensen, T., Le Roux, L.: Rewriting approximations for fast prototyping of static analyzers. In: Baader, F. (ed.) RTA 2007. LNCS, vol. 4533, pp. 48–62. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  4. Cortier, V., Delaune, S., Lafourcade, P.: A Survey of Algebraic Properties Used in Cryptographic Protocols. Journal of Computer Security 14(1), 1–43 (2006)

    Article  Google Scholar 

  5. D’Silva, V., Kroening, D., Weissenbacher, G.: A Survey of Automated Techniques for Formal Software Verification. IEEE Transactions Computer-Aided Design of Integrated Circuits and Systems 27(7), 1165–1178 (2008)

    Article  Google Scholar 

  6. Falke, S., Kapur, D.: Dependency Pairs for rewriting with non-free constructors. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 426–442. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  7. Falke, S., Kapur, D.: Inductive decidability using implicit induction. In: Hermann, M., Voronkov, A. (eds.) LPAR 2006. LNCS (LNAI), vol. 4246, pp. 45–59. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  8. Falke, S., Kapur, D.: Termination of context-sensitive rewriting with built-in numbers and collection data structures. In: Escobar, S. (ed.) WFLP 2009. LNCS, vol. 5979, pp. 44–61. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  9. Futatsugi, K., Goguen, J.A., Jouannaud, J.-P., Meseguer, J.: Principles of OBJ2. In: Proceedings of the International Symposium POPL, pp. 52–66 (1985)

    Google Scholar 

  10. Genet, T.: Decidable approximations of sets of descendants and sets of normal forms. In: Nipkow, T. (ed.) RTA 1998. LNCS, vol. 1379, pp. 151–165. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  11. Genet, T.: Reachability Analysis of Rewriting for Software Verification. Université de Rennes 1 (2009), Habilitation document. http://www.irisa.fr/celtique/genet/publications.html

  12. Genet, T., Rusu, V.: Equational Approximations for Tree Automata Completion. Journal of Symbolic Computation 45(5), 574–597 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Genet, T., Salmon, Y.: Reachability analysis of innermost rewriting. In: Proceedings of the International Conference RTA. LIPIcs, vol. 36, pp. 177–193 (2015)

    Google Scholar 

  14. Kochems, J., Ong, C.-H.L.: Improved functional flow and reachability analyses using indexed linear tree grammars. In: Proceedings of the International Conference RTA. LIPIcs, vol. 10, pp. 187–202 (2011)

    Google Scholar 

  15. Kojima, Y., Sakai, M.: Innermost reachability and context sensitive reachability properties are decidable for linear right-shallow term rewriting systems. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 187–201. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  16. Lucas, S.: Context-sensitive computations in functional and functional logic programs. Journal of Functional and Logic Programming 1998(1), January 1998

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pierre Réty .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Andrianarivelo, N., Réty, P. (2015). Over-Approximating Terms Reachable by Context-Sensitive Rewriting. In: Bojanczyk, M., Lasota, S., Potapov, I. (eds) Reachability Problems. RP 2015. Lecture Notes in Computer Science(), vol 9328. Springer, Cham. https://doi.org/10.1007/978-3-319-24537-9_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-24537-9_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24536-2

  • Online ISBN: 978-3-319-24537-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics