Skip to main content
Book cover

International Conference on Computer Aided Verification

CAV 2014: Computer Aided Verification pp 150–166Cite as

String Constraints for Verification

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8559)

Abstract

We present a decision procedure for a logic that combines (i) word equations over string variables denoting words of arbitrary lengths, together with (ii) constraints on the length of words, and on (iii) the regular languages to which words belong. Decidability of this general logic is still open. Our procedure is sound for the general logic, and a decision procedure for a particularly rich fragment that restricts the form in which word equations are written. In contrast to many existing procedures, our method does not make assumptions about the maximum length of words. We have developed a prototypical implementation of our decision procedure, and integrated it into a CEGAR-based model checker for the analysis of programs encoded as Horn clauses. Our tool is able to automatically establish the correctness of several programs that are beyond the reach of existing methods.

Keywords

  • Model Check
  • Inference Rule
  • Decision Procedure
  • Regular Expression
  • Regular Language

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Supported by the Uppsala Programming for Multicore Architectures Research Center (UPMARC), the Czech Science Foundation (13-37876P), Brno University of Technology (FIT-S-12-1, FIT-S-14-2486), and the Linköping CENIIT Center (12.04).

Download conference paper PDF

References

  1. Angluin, D.: Learning regular sets from queries and counterexamples. Inf. Comput. 75(2), 87–106 (1987)

    CrossRef  MATH  MathSciNet  Google Scholar 

  2. Ball, T., Levin, V., Rajamani, S.K.: A decade of software model checking with slam. Commun. ACM 54(7), 68–76 (2011)

    CrossRef  Google Scholar 

  3. Brillout, A., Kroening, D., Rümmer, P., Wahl, T.: An interpolating sequent calculus for quantifier-free Presburger arithmetic. Journal of Automated Reasoning 47, 341–367 (2011)

    CrossRef  MATH  MathSciNet  Google Scholar 

  4. Büchi, J.R., Senger, S.: Definability in the existential theory of concatenation and undecidable extensions of this theory. Z. Math. Logik Grundlagen Math. 34(4) (1988)

    Google Scholar 

  5. Cimatti, A., Griggio, A., Schaafsma, B.J., Sebastiani, R.: The mathSAT5 SMT solver. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 93–107. Springer, Heidelberg (2013)

    Google Scholar 

  6. Craig, W.: Linear reasoning. A new form of the Herbrand-Gentzen theorem. The Journal of Symbolic Logic 22(3) (1957)

    Google Scholar 

  7. de Moura, L., Bjørner, N.S.: Z3: An Efficient SMT Solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  8. D’Silva, V., Kroening, D., Weissenbacher, G.: A survey of automated techniques for formal software verification. IEEE Trans. on CAD of Integrated Circuits and Systems 27(7), 1165–1178 (2008)

    CrossRef  Google Scholar 

  9. Ganesh, V., Dill, D.L.: A decision procedure for bit-vectors and arrays. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 519–531. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  10. Ganesh, V., Minnes, M., Solar-Lezama, A., Rinard, M.: Word equations with length constraints: What’s decidable? In: Biere, A., Nahir, A., Vos, T. (eds.) HVC. LNCS, vol. 7857, pp. 209–226. Springer, Heidelberg (2013)

    Google Scholar 

  11. Graf, S., Saidi, H.: Construction of abstract state graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72–83. Springer, Heidelberg (1997)

    CrossRef  Google Scholar 

  12. Grebenshchikov, S., Lopes, N.P., Popeea, C., Rybalchenko, A.: Synthesizing software verifiers from proof rules. In: PLDI, pp. 405–416 (2012)

    Google Scholar 

  13. Henzinger, T.A., Jhala, R., Majumdar, R., McMillan, K.L.: Abstractions from proofs. In: 31st POPL (2004)

    Google Scholar 

  14. Hojjat, H., Konečný, F., Garnier, F., Iosif, R., Kuncak, V., Rümmer, P.: A verification toolkit for numerical transition systems. In: Giannakopoulou, D., Méry, D. (eds.) FM 2012. LNCS, vol. 7436, pp. 247–251. Springer, Heidelberg (2012)

    CrossRef  Google Scholar 

  15. Jhala, R., Majumdar, R.: Software model checking. ACM Comput. Surv. 41(4) (2009)

    Google Scholar 

  16. Jhala, R., McMillan, K.L.: A practical and complete approach to predicate refinement. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 459–473. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  17. Kieżun, A., Ganesh, V., Artzi, S., Guo, P.J., Hooimeijer, P., Ernst, M.D.: HAMPI: A solver for word equations over strings, regular expressions, and context-free grammars. ACM Transactions on Software Engineering and Methodology 21(4) (2012)

    Google Scholar 

  18. Makanin, G.S.: The problem of solvability of equations in a free semigroup. Mathematics of the USSR-Sbornik 32(2), 129–198 (1977)

    CrossRef  MATH  Google Scholar 

  19. McMillan, K.L.: Lazy abstraction with interpolants. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 123–136. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  20. Méndez-Lojo, M., Navas, J., Hermenegildo, M.V.: A flexible (C)LP-based approach to the analysis of object-oriented programs. In: King, A. (ed.) LOPSTR 2007. LNCS, vol. 4915, pp. 154–168. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  21. Møller, A.: dk.brics.automaton – finite-state automata and regular expressions for Java (2010), http://www.brics.dk/automaton/

  22. Rümmer, P., Hojjat, H., Kuncak, V.: Classifying and solving horn clauses for verification. In: Cohen, E., Rybalchenko, A. (eds.) VSTTE 2013. LNCS, vol. 8164, pp. 1–21. Springer, Heidelberg (2014)

    CrossRef  Google Scholar 

  23. Saxena, P., Akhawe, D., Hanna, S., Mao, F., McCamant, S., Song, D.: A Symbolic Execution Framework for JavaScript. In: IEEE Symposium on Security and Privacy, pp. 513–528. IEEE Computer Society (2010)

    Google Scholar 

  24. Saxena, P., Hanna, S., Poosankam, P., Song, D.: FLAX: Systematic discovery of client-side validation vulnerabilities in rich web applications. In: NDSS. The Internet Society (2010)

    Google Scholar 

  25. Yu, F., Alkhalaf, M., Bultan, T.: Stranger: An automata-based string analysis tool for PHP. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 154–157. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  26. Zheng, Y., Zhang, X., Ganesh, V.: Z3-str: A Z3-based string solver for web application analysis. In: Proceedings of the 2013 9th Joint Meeting on Foundations of Software Engineering, ESEC/FSE 2013, pp. 114–124. ACM, New York (2013)

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information Technology, Uppsala University, Sweden

    Parosh Aziz Abdulla, Mohamed Faouzi Atig, Philipp Rümmer & Jari Stenman

  2. Institute of Information Science, Academia Sinica, Taiwan

    Yu-Fang Chen

  3. Faculty of Information Technology, Brno University of Technology, Czech Republic

    Lukáš Holík

  4. Department of Computer and Information Science, Linköping University, Sweden

    Ahmed Rezine

Authors
  1. Parosh Aziz Abdulla
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohamed Faouzi Atig
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yu-Fang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lukáš Holík
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ahmed Rezine
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Philipp Rümmer
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Jari Stenman
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Johannes Kepler University Linz, Altenberger Str. 69, 4040, Linz, Austria

    Armin Biere

  2. IAIK, Graz University of Technology, Inffeldgasse 16a, 8010, Graz, Austria

    Roderick Bloem

Rights and permissions

Reprints and Permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Abdulla, P.A. et al. (2014). String Constraints for Verification. In: Biere, A., Bloem, R. (eds) Computer Aided Verification. CAV 2014. Lecture Notes in Computer Science, vol 8559. Springer, Cham. https://doi.org/10.1007/978-3-319-08867-9_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-08867-9_10

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08866-2

  • Online ISBN: 978-3-319-08867-9

  • eBook Packages: Computer ScienceComputer Science (R0)