A DPLL(T) Theory Solver for a Theory of Strings and Regular Expressions

  • Tianyi Liang
  • Andrew Reynolds
  • Cesare Tinelli
  • Clark Barrett
  • Morgan Deters
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8559)

Abstract

An increasing number of applications in verification and security rely on or could benefit from automatic solvers that can check the satisfiability of constraints over a rich set of data types that includes character strings. Unfortunately, most string solvers today are standalone tools that can reason only about (some fragment) of the theory of strings and regular expressions, sometimes with strong restrictions on the expressiveness of their input language. These solvers are based on reductions to satisfiability problems over other data types, such as bit vectors, or to automata decision problems. We present a set of algebraic techniques for solving constraints over the theory of unbounded strings natively, without reduction to other problems. These techniques can be used to integrate string reasoning into general, multi-theory SMT solvers based on the DPLL(T) architecture. We have implemented them in our SMT solver cvc4 to expand its already large set of built-in theories to a theory of strings with concatenation, length, and membership in regular languages. Our initial experimental results show that, in addition, over pure string problems, cvc4 is highly competitive with specialized string solvers with a comparable input language.

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References

  1. 1.
    Barrett, C., Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Splitting on demand in SAT modulo theories. In: Hermann, M., Voronkov, A. (eds.) LPAR 2006. LNCS (LNAI), vol. 4246, pp. 512–526. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  2. 2.
    Barrett, C., Sebastiani, R., Seshia, S., Tinelli, C.: Satisfiability modulo theories. In: Biere, A., Heule, M.J.H., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability, vol. 185, ch. 26, pp. 825–885. IOS Press (February 2009)Google Scholar
  3. 3.
    Bjørner, N., Tillmann, N., Voronkov, A.: Path feasibility analysis for string-manipulating programs. In: Kowalewski, S., Philippou, A. (eds.) TACAS 2009. LNCS, vol. 5505, pp. 307–321. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  4. 4.
    Christensen, A.S., Møller, A., Schwartzbach, M.I.: Precise analysis of string expressions. In: Cousot, R. (ed.) SAS 2003. LNCS, vol. 2694, pp. 1–18. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Fu, X., Li, C.: A string constraint solver for detecting web application vulnerability. In: Proceedings of the 22nd International Conference on Software Engineering and Knowledge Engineering, SEKE 2010, Knowledge Systems Institute Graduate School (2010)Google Scholar
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    Ghosh, I., Shafiei, N., Li, G., Chiang, W.-F.: JST: An automatic test generation tool for industrial Java applications with strings. In: Proceedings of the 2013 International Conference on Software Engineering, ICSE 2013, pp. 992–1001. IEEE Press (2013)Google Scholar
  8. 8.
    Hooimeijer, P., Veanes, M.: An evaluation of automata algorithms for string analysis. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 248–262. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. 9.
    Hooimeijer, P., Weimer, W.: A decision procedure for subset constraints over regular languages. In: Proceedings of the 2009 ACM SIGPLAN Conference on Programming Language Design and Implementation, pp. 188–198. ACM (2009)Google Scholar
  10. 10.
    Hooimeijer, P., Weimer, W.: Solving string constraints lazily. In: Proceedings of the IEEE/ACM International Conference on Automated Software Engineering, pp. 377–386. ACM (2010)Google Scholar
  11. 11.
    Kiezun, A., Ganesh, V., Guo, P.J., Hooimeijer, P., Ernst, M.D.: HAMPI: a solver for string constraints. In: Proceedings of the Eighteenth International Symposium on Software Testing and Analysis, pp. 105–116. ACM (2009)Google Scholar
  12. 12.
    Li, G., Ghosh, I.: PASS: String solving with parameterized array and interval automaton. In: Bertacco, V., Legay, A. (eds.) HVC 2013. LNCS, vol. 8244, pp. 15–31. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  13. 13.
    Liang, T., Reynolds, A., Tinelli, C., Barrett, C., Deters, M.: A DPLL(T) theory solver for a theory of strings and regular expressions. Technical report, Department of Computer Science, The University of Iowa (2014), http://cvc4.cs.nyu.edu/papers/CAV2014-strings/
  14. 14.
    Makanin, G.S.: The problem of solvability of equations in a free semigroup. English transl. in Math USSR Sbornik 32, 147–236 (1977)MathSciNetGoogle Scholar
  15. 15.
    Nelson, G., Oppen, D.C.: Simplification by cooperating decision procedures. ACM Trans. on Programming Languages and Systems 1(2), 245–257 (1979)CrossRefMATHGoogle Scholar
  16. 16.
    Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT Modulo Theories: from an abstract Davis-Putnam-Logemann-Loveland Procedure to DPLL(T). Journal of the ACM 53(6), 937–977 (2006)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Plandowski, W.: Satisfiability of word equations with constants is in PSPACE. Journal of the ACM 51(3), 483–496 (2004)CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Saxena, P., Akhawe, D.: Kaluza web site (2010), http://webblaze.cs.berkeley.edu/2010/kaluza/
  19. 19.
    Saxena, P., Akhawe, D., Hanna, S., Mao, F., McCamant, S., Song, D.: A symbolic execution framework for JavaScript. In: Proceedings of the 2010 IEEE Symposium on Security and Privacy, pp. 513–528. IEEE Computer Society (2010)Google Scholar
  20. 20.
    Tillmann, N., de Halleux, J.: Pex–white box test generation for. NET. In: Beckert, B., Hähnle, R. (eds.) TAP 2008. LNCS, vol. 4966, pp. 134–153. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  21. 21.
    Veanes, M.: Applications of symbolic finite automata. In: Konstantinidis, S. (ed.) CIAA 2013. LNCS, vol. 7982, pp. 16–23. Springer, Heidelberg (2013)Google Scholar
  22. 22.
    Veanes, M., Bjørner, N., de Moura, L.: Symbolic automata constraint solving. In: Fermüller, C.G., Voronkov, A. (eds.) LPAR-17. LNCS, vol. 6397, pp. 640–654. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  23. 23.
    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)CrossRefGoogle Scholar
  24. 24.
    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. ESEC/FSE 2013, pp. 114–124. ACM (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Tianyi Liang
    • 1
  • Andrew Reynolds
    • 1
  • Cesare Tinelli
    • 1
  • Clark Barrett
    • 2
  • Morgan Deters
    • 2
  1. 1.Department of Computer ScienceThe University of IowaUSA
  2. 2.Department of Computer ScienceNew York UniversityUSA

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