Skip to main content
SpringerLink
Log in
Book cover

Working Conference on Verified Software: Theories, Tools, and Experiments

VSTTE 2018: Verified Software. Theories, Tools, and Experiments pp 309–321Cite as

Loop Detection by Logically Constrained Term Rewriting

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11294))

Abstract

Logically constrained rewrite systems constitute a very general rewriting formalism that can capture simplification processes in various domains as well as computation in imperative programs. In both of these contexts, nontermination is a critical source of errors. We present new criteria to find loops in logically constrained rewrite systems which are implemented in the tool Ctrl. We illustrate the usefulness of these criteria in three example applications: to find loops in LLVM peephole optimizations, to detect looping executions of C programs, and to establish nontermination of integer transition systems.

This work is partially supported by JSPS KAKENHI Grant Number JP18K11160 and FWF (Austrian Science Fund) project T789.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Learn about institutional subscriptions

Notes

  1. 1.

    http://cl-informatik.uibk.ac.at/users/swinkler/lctrs_loops.

  2. 2.

    http://termination-portal.org/wiki/TPDB.

  3. 3.

    http://www.termination-portal.org/wiki/Termination_Competition_2017.

References

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

    Book  Google Scholar 

  2. Borralleras, C., Brockschmidt, M., Larraz, D., Oliveras, A., Rodríguez-Carbonell, E., Rubio, A.: Proving termination through conditional termination. In: Legay, A., Margaria, T. (eds.) TACAS 2017. Heidelberg, vol. 10205, pp. 99–117. Springer, Cham (2017). https://doi.org/10.1007/978-3-662-54577-5_6

    Chapter  Google Scholar 

  3. Brockschmidt, M., Cook, B., Ishtiaq, S., Khlaaf, H., Piterman, N.: T2: Temporal property verification. In: Chechik, M., Raskin, J.-F. (eds.) TACAS 2016. LNCS, vol. 9636, pp. 387–393. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49674-9_22

    Chapter  Google Scholar 

  4. Falke, S., Kapur, D.: A term rewriting approach to the automated termination analysis of imperative programs. In: Schmidt, R.A. (ed.) CADE 2009. LNCS (LNAI), vol. 5663, pp. 277–293. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02959-2_22

    Chapter  MATH  Google Scholar 

  5. Falke, S., Kapur, D., Sinz, C.: Termination analysis of C programs using compiler intermediate languages. In: Proceedings of the 22nd RTA, Leibniz International Proceedings in Informatics, vol. 10, pp. 41–50 (2011). https://doi.org/10.4230/LIPIcs.RTA.2011.41

  6. Fuhs, C., Giesl, J., Plücker, M., Schneider-Kamp, P., Falke, S.: Proving termination of integer term rewriting. In: Treinen, R. (ed.) RTA 2009. LNCS, vol. 5595, pp. 32–47. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02348-4_3

    Chapter  MATH  Google Scholar 

  7. Fuhs, C., Kop, C., Nishida, N.: Verifying procedural programs via constrained rewriting induction. ACM TOCL 18(2), 14:1–14:50 (2017). https://doi.org/10.1145/3060143

    Article  MathSciNet  MATH  Google Scholar 

  8. Ganesh, V., Berezin, S., Dill, D.: A decision procedure for fixed-width bit-vectors. Technical report, Stanford University (2005)

    Google Scholar 

  9. Giesl, J., et al.: Analyzing program termination and complexity automatically with AProVE. JAR 58(1), 3–31 (2017). https://doi.org/10.1007/s10817-016-9388-y

    Article  MathSciNet  MATH  Google Scholar 

  10. Gupta, A., Henzinger, T., Majumdar, R., Rybalchenko, A., Xu, R.G.: Proving non-termination. SIGPLAN Not. 43(1), 147–158 (2008). https://doi.org/10.1145/1328897.1328459

    Article  MATH  Google Scholar 

  11. Hoder, K., Khasidashvili, Z., Korovin, K., Voronkov, A.: Preprocessing techniques for first-order clausification. In: Proceedings of the 12th FMCAD, pp. 44–51 (2012)

    Google Scholar 

  12. Kop, C., Nishida, N.: Term rewriting with logical constraints. In: Fontaine, P., Ringeissen, C., Schmidt, R.A. (eds.) FroCoS 2013. LNCS (LNAI), vol. 8152, pp. 343–358. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40885-4_24

    Chapter  Google Scholar 

  13. Kop, C., Nishida, N.: Constrained term rewriting tooL. In: Davis, M., Fehnker, A., McIver, A., Voronkov, A. (eds.) LPAR 2015. LNCS, vol. 9450, pp. 549–557. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48899-7_38

    Chapter  Google Scholar 

  14. Lopes, N., Menendez, D., Nagarakatte, S., Regehr, J.: Provably correct peephole optimizations with Alive. In: Proceedings of the 36th PLDI, pp. 22–32 (2015). https://doi.org/10.1145/2737924.2737965

  15. Lopes, N., Menendez, D., Nagarakatte, S., Regehr, J.: Practical verification of peephole optimizations with Alive. Commun. ACM 61(2), 84–91 (2018). https://doi.org/10.1145/3166064

    Article  Google Scholar 

  16. Menendez, D., Nagarakatte, S.: Termination-checking for LLVM peephole optimizations. In: Proceedings of the 38th International Conference on Software Engineering, pp. 191–202 (2016). https://doi.org/10.1145/2884781.2884809

  17. Nadel, A.: Bit-vector rewriting with automatic rule generation. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 663–679. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08867-9_44

    Chapter  Google Scholar 

  18. Nishida, N., Sakai, M., Hattori, T.: On disproving termination of constrained term rewriting systems. In: Proceedings of the 11th WST (2010)

    Google Scholar 

  19. Payet, É.: Loop detection in term rewriting using the eliminating unfoldings. Theor. Comput. Sci. 403(2–3), 307–327 (2008). https://doi.org/10.1016/j.tcs.2008.05.013

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors thank the anonymous referees for their helpful comments.

Author information

Authors and Affiliations

  1. Department of Computing and Software Systems, Graduate School of Informatics, Nagoya University, Nagoya, Japan

    Naoki Nishida

  2. Department of Computer Science, University of Innsbruck, Innsbruck, Austria

    Sarah Winkler

Authors
  1. Naoki Nishida
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sarah Winkler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sarah Winkler .

Editor information

Editors and Affiliations

  1. Yale University, New Haven, CT, USA

    Ruzica Piskac

  2. Uppsala University, Uppsala, Sweden

    Philipp Rümmer

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Nishida, N., Winkler, S. (2018). Loop Detection by Logically Constrained Term Rewriting. In: Piskac, R., Rümmer, P. (eds) Verified Software. Theories, Tools, and Experiments. VSTTE 2018. Lecture Notes in Computer Science(), vol 11294. Springer, Cham. https://doi.org/10.1007/978-3-030-03592-1_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-03592-1_18

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-03591-4

  • Online ISBN: 978-3-030-03592-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation