Abstract
Using dashed strings is an approach recently introduced in Constraint Programming (CP) to represent the domain of string variables, when solving combinatorial problems with string constraints. One of the most important string constraints is that of regular membership: \(\textsc {regular} (x, R)\) imposes string x to be a member of the regular language defined by automaton R. The regular constraint is useful for specifying complex constraints on fixed length finite sequences, and regularly appears in CP models. Dealing with regular is also desirable in software testing and verification, because regular expressions are often used in modern programming languages for pattern matching. In this paper, we define a regular propagator for dashed string solvers. We show that this propagator, implemented in the G-Strings solver, is substantially better than the current state-of-the-art. We also demonstrate that many regular constraints appearing in string solving benchmarks can actually be tackled by dashed strings solvers without explicitly using regular.
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Notes
- 1.
Note that \(maxl(R) \ne \max \{ |w| ~|~ w \in L(R), |w| \le \lambda \}\), which is less easy to compute. If \(maxl(R) > \lambda \), we set \(maxl(R) = \lambda \): this is a correct but not optimal upper bound.
- 2.
Note this is different from the iterated concatenation of strings. For example, encoding
with 
is unsound because this actually encodes the constraint 
(e.g., 
). - 3.
We used Z3str3 4.6.2 and CVC4 1.5. The source code of the experiments is publicly available at: https://bitbucket.org/robama/exp_cp_2018.
- 4.
Precisely, this is the instance 489 of the HammingDistance class. G-Decomp with \(\lambda = 500\) takes 454.6 s to detect the unsatisfiability. Clearly, we can only prove that there is no solution where all string variables x have length \(|x| \le \lambda \).
with 
is unsound because this actually encodes the constraint 
(e.g., 
).References
Abdulla, P.A., Atig, M.F., Chen, Y., Diep, B.P., HolÃk, L., Rezine, A., Rümmer, P.: Flatten and conquer: a framework for efficient analysis of string constraints. In: Proceedings of the 38th ACM SIGPLAN Conference on Programming Language Design and Implementation PLDI 2017, pp. 602–617, Barcelona, Spain, 18–23 June 2017 (2017)
Abdulla, P.A., Atig, M.F., Chen, Y.-F., HolÃk, L., Rezine, A., Rümmer, P., Stenman, J.: Norn: an SMT solver for string constraints. In: Kroening, D., Păsăreanu, C.S. (eds.) CAV 2015. LNCS, vol. 9206, pp. 462–469. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21690-4_29
Amadini, R., Flener, P., Pearson, J., Scott, J.D., Stuckey, P.J., Tack, G.: MiniZinc with Strings. In: Logic-Based Program Synthesis and Transformation - 25th International Symposium LOPSTR 2016 (2016). https://arxiv.org/abs/1608.03650
Amadini, R., Gange, G., Stuckey, P.J.: Propagating lex, find and replace with dashed strings. In: van Hoeve, W.-J. (ed.) CPAIOR 2018. LNCS, vol. 10848, pp. 18–34. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93031-2_2
Amadini, R., Gange, G., Stuckey, P.J.: Sweep-based propagation for string cosntraint solving. In: To appear in AAAI 2018 (2018)
Amadini, R., Gange, G., Stuckey, P.J., Tack, G.: A novel approach to string constraint solving. In: Beck, J.C. (ed.) CP 2017. LNCS, vol. 10416, pp. 3–20. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66158-2_1
Barták, R.: Modelling resource transitions in constraint-based scheduling. In: Grosky, W.I., Plášil, F. (eds.) SOFSEM 2002. LNCS, vol. 2540, pp. 186–194. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-36137-5_13
Beldiceanu, N., Carlsson, M., Demassey, S., Petit, T.: Global constraint catalogue: past, present and future. Constraints 12(1), 21–62 (2007). http://sofdem.github.io/gccat/
Berzish, M., Zheng, Y., Ganesh, V.: Z3str3: A string solver with theory-aware branching. CoRR abs/1704.07935 (2017). http://arxiv.org/abs/1704.07935
Cheng, K.C.K., Yap, R.H.C.: Maintaining generalized arc consistency on Ad Hoc r-ary constraints. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 509–523. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85958-1_34
Gecode Team: Gecode: Generic constraint development environment (2016). http://www.gecode.org
HolÃk, L., Janku, P., Lin, A.W., Rümmer, P., Vojnar, T.: String constraints with concatenation and transducers solved efficiently. PACMPL 2(POPL), 4:1–4:32 (2018)
IBM: Security AppScan (2018). https://www.ibm.com/security/application-security/appscan
Liang, T., Reynolds, A., Tinelli, C., Barrett, C., Deters, M.: A DPLL(T) theory solver for a theory of strings and regular expressions. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 646–662. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08867-9_43
Martens, W., Niewerth, M., Schwentick, T.: Schema design for XML repositories: complexity and tractability. In: Paredaens, J., Gucht, D.V. (eds.) Proceedings of the Twenty-Ninth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, PODS 2010, Indianapolis, Indiana, USA, pp. 239–250. ACM, 6–11 June 2010 (2010)
Perez, G., Régin, J.-C.: Improving GAC-4 for table and MDD constraints. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 606–621. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10428-7_44
Pesant, G.: A regular language membership constraint for finite sequences of variables. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 482–495. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30201-8_36
Scott, J.D., Flener, P., Pearson, J., Schulte, C.: Design and implementation of bounded-length sequence variables. In: Salvagnin, D., Lombardi, M. (eds.) CPAIOR 2017. LNCS, vol. 10335, pp. 51–67. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59776-8_5
Tateishi, T., Pistoia, M., Tripp, O.: Path- and index-sensitive string analysis based on monadic second-order logic. ACM Trans. Softw. Eng. Methodol. 22(4), 33 (2013)
Thomé, J., Shar, L.K., Bianculli, D., Briand, L.C.: Search-driven string constraint solving for vulnerability detection. In: Proceedings of the 39th International Conference on Software Engineering ICSE 2017, Buenos Aires, Argentina, pp. 198–208, 20–28 May 2017 (2017)
Trinh, M., Chu, D., Jaffar, J.: S3: a symbolic string solver for vulnerability detection in web applications. In: SIGSAC, pp. 1232–1243. ACM (2014)
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). https://doi.org/10.1007/978-3-642-12002-2_13
Acknowledgments
This work is supported by the Australian Research Council (ARC) through Linkage Project Grant LP140100437 and Discovery Early Career Researcher Award DE160100568.
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Amadini, R., Gange, G., Stuckey, P.J. (2018). Propagating Regular Membership with Dashed Strings. In: Hooker, J. (eds) Principles and Practice of Constraint Programming. CP 2018. Lecture Notes in Computer Science(), vol 11008. Springer, Cham. https://doi.org/10.1007/978-3-319-98334-9_2
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