Abstract
While model checking safety of infinite-state systems by inferring state invariants has steadily improved recently, most verification tools still rely on a technique based on bounded model checking to detect safety violations. In particular, the current techniques typically analyze executions by unfolding transitions one step at a time, and the slow growth of execution length prevents detection of deep counterexamples before the tool reaches its limits on computations. We propose a novel model-checking algorithm that is capable of both proving unbounded safety and finding long counterexamples. The idea is to use Craig interpolation to guide the creation of symbolic abstractions of exponentially longer sequences of transitions. Our experimental analysis shows that on unsafe benchmarks with deep counterexamples our implementation can detect faulty executions that are at least an order of magnitude longer than those detectable by the state-of-the-art tools.
The first author is partially funded by the project 20-07487S of the Czech Science Foundation. The first, third, and forth authors are partially funded by the Swiss National Science Foundation project 200021_185031. The second author is partially funded by the gift from Amazon Web Services.
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Alt, L., Asadi, S., Chockler, H., Even Mendoza, K., Fedyukovich, G., Hyvärinen, A.E.J., Sharygina, N.: Hifrog: SMT-based function summarization for software verification. In: Legay, A., Margaria, T. (eds.) Tools and Algorithms for the Construction and Analysis of Systems. pp. 207–213. Springer Berlin Heidelberg, Berlin, Heidelberg (2017)
Alt, L., Hyvärinen, A.E.J., Sharygina, N.: LRA interpolants from no man’s land. In: Strichman, O., Tzoref-Brill, R. (eds.) HVC 2017. LNCS, vol. 10629, pp. 195–210. Springer, Cham (2017)
Asadi, S., Blicha, M., Fedyukovich, G., Hyv\(\backslash \)”arinen, A., Even-Mendoza, K., Sharygina, N., Chockler, H.: Function summarization modulo theories. In: Barthe, G., Sutcliffe, G., Veanes, M. (eds.) LPAR-22. 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning. EPiC Series in Computing, vol. 57, pp. 56–75. EasyChair (2018)
Asadi, S., Blicha, M., Hyvärinen, A.E.J., Fedyukovich, G., Sharygina, N.: Incremental verification by SMT-based summary repair. In: 2020 Formal Methods in Computer Aided Design, FMCAD 2020, Haifa, Israel, September 21-24, 2020. pp. 77–82. IEEE (2020)
Bardin, S., Finkel, A., Leroux, J., Petrucci, L.: Fast: Acceleration from theory to practice. International Journal on Software Tools for Technology Transfer 10(5), 401–424 (2008)
Barrett, C., Fontaine, P., Tinelli, C.: The SMT-LIB Standard: Version 2.6. Tech. rep., Department of Computer Science, The University of Iowa (2017), available at http://smtlib.cs.uiowa.edu
Barrett, C., de Moura, L., Ranise, S., Stump, A., Tinelli, C.: The SMT-LIB initiative and the rise of SMT. In: Barner, S., Harris, I., Kroening, D., Raz, O. (eds.) Hardware and Software: Verification and Testing. pp. 3–3. Springer Berlin Heidelberg, Berlin, Heidelberg (2011)
Beyer, D., Dangl, M., Wendler, P.: A unifying view on SMT-based software verification. Journal of Automated Reasoning 60(3), 299–335 (Mar 2018)
Biere, A., Cimatti, A., Clarke, E.M., Zhu, Y.: Symbolic Model Checking without BDDs. In: Tools and Alg. for the Const. and Anal. of Systems (TACAS ’99). LNCS, vol. 1579, pp. 193–207 (1999)
Bjørner, N., Janota, M.: Playing with quantified satisfaction. In: Fehnker, A., McIver, A., Sutcliffe, G., Voronkov, A. (eds.) LPAR-20. 20th International Conferences on Logic for Programming, Artificial Intelligence and Reasoning - Short Presentations. EPiC Series in Computing, vol. 35, pp. 15–27. EasyChair (2015)
Blicha, M., Hyvärinen, A.E.J., Kofroň, J., Sharygina, N.: Decomposing Farkas interpolants. In: Vojnar, T., Zhang, L. (eds.) Proc. TACAS 2019. LNCS, vol. 11427, pp. 3–20. Springer (2019)
Bozga, M., Iosif, R., Konečný, F.: Fast acceleration of ultimately periodic relations. In: Touili, T., Cook, B., Jackson, P. (eds.) Computer Aided Verification. pp. 227–242. Springer Berlin Heidelberg, Berlin, Heidelberg (2010)
Caniart, N., Fleury, E., Leroux, J., Zeitoun, M.: Accelerating interpolation-based model-checking. In: Ramakrishnan, C.R., Rehof, J. (eds.) Tools and Algorithms for the Construction and Analysis of Systems. pp. 428–442. Springer Berlin Heidelberg, Berlin, Heidelberg (2008)
Cimatti, A., Griggio, A.: Software model checking via IC3. In: Madhusudan, P., Seshia, S.A. (eds.) Computer Aided Verification. pp. 277–293. Springer Berlin Heidelberg, Berlin, Heidelberg (2012)
Cimatti, A., Griggio, A., Mover, S., Tonetta, S.: IC3 modulo theories via implicit predicate abstraction. In: Ábrahám, E., Havelund, K. (eds.) Tools and Algorithms for the Construction and Analysis of Systems. pp. 46–61. Springer Berlin Heidelberg, Berlin, Heidelberg (2014)
Cimatti, A., Griggio, A., Sebastiani, R.: Efficient generation of Craig interpolants in satisfiability modulo theories. ACM Trans. Comput. Logic 12(1), 7:1–7:54 (Nov 2010)
Clarke, E.M., Henzinger, T.A., Veith, H., Bloem, R. (eds.): Handbook of Model Checking. Springer (2018)
Craig, W.: Three uses of the Herbrand-Gentzen theorem in relating model theory and proof theory. The Journal of Symbolic Logic 22(3), 269–285 (1957)
D’Silva, V., Kroening, D., Purandare, M., Weissenbacher, G.: Interpolant strength. In: VMCAI 2010. LNCS, vol. 5944, pp. 129–145. Springer (2010)
Fedyukovich, G., Bodík, R.: Accelerating syntax-guided invariant synthesis. In: TACAS, Part I. LNCS, vol. 10805, pp. 251–269. Springer (2018)
Fedyukovich, G., Rümmer, P.: Competition report: CHC-COMP-21. In: Hojjat, H., Kafle, B. (eds.) Proceedings 8th Workshop on Horn Clauses for Verification and Synthesis, HCVS@ETAPS 2021, Virtual, 28th March 2021. EPTCS, vol. 344, pp. 91–108 (2021)
Frohn, F.: A calculus for modular loop acceleration. In: Biere, A., Parker, D. (eds.) Tools and Algorithms for the Construction and Analysis of Systems. pp. 58–76. Springer International Publishing, Cham (2020)
Govind, H., Fedyukovich, G., Gurfinkel, A.: Word level property directed reachability. In: 2020 IEEE/ACM International Conference On Computer Aided Design (ICCAD). pp. 1–9 (2020)
Hojjat, H., Iosif, R., Konečný, F., Kuncak, V., Rümmer, P.: Accelerating interpolants. In: Chakraborty, S., Mukund, M. (eds.) Automated Technology for Verification and Analysis. pp. 187–202. Springer Berlin Heidelberg, Berlin, Heidelberg (2012)
Hojjat, H., Rümmer, P.: The ELDARICA Horn Solver. In: FMCAD. pp. 158–164. IEEE (2018)
Hyvärinen, A.E.J., Marescotti, M., Alt, L., Sharygina, N.: OpenSMT2: An SMT solver for multi-core and cloud computing. In: Creignou, N., Le Berre, D. (eds.) SAT 2016. LNCS, vol. 9710, pp. 547–553. Springer, Cham (2016)
Jhala, R., McMillan, K.L.: Interpolant-based transition relation approximation. In: Etessami, K., Rajamani, S.K. (eds.) Computer Aided Verification. pp. 39–51. Springer Berlin Heidelberg, Berlin, Heidelberg (2005)
Jovanovic, D., Dutertre, B.: Property-directed \(k\)-induction. In: Piskac, R., Talupur, M. (eds.) Proc. FMCAD 2016. pp. 85–92. IEEE (2016)
Komuravelli, A., Bjørner, N., Gurfinkel, A., McMillan, K.L.: Compositional verification of procedural programs using Horn clauses over integers and arrays. In: 2015 Formal Methods in Computer-Aided Design (FMCAD). pp. 89–96 (2015)
Komuravelli, A., Gurfinkel, A., Chaki, S.: SMT-based model checking for recursive programs. Formal Methods in System Design 48(3), 175–205 (Jun 2016)
Krajíček, J.: Interpolation theorems, lower bounds for proof systems, and independence results for bounded arithmetic. The Journal of Symbolic Logic 62(2), 457–486 (1997)
Kroening, D., Lewis, M., Weissenbacher, G.: Under-approximating loops in C programs for fast counterexample detection. Formal Methods in System Design 47(1), 75–92 (2015)
Kroening, D., Sharygina, N., Tsitovich, A., Wintersteiger, C.M.: Termination analysis with compositional transition invariants. In: Touili, T., Cook, B., Jackson, P. (eds.) Computer Aided Verification. pp. 89–103. Springer Berlin Heidelberg, Berlin, Heidelberg (2010)
McMillan, K.L.: Interpolation and SAT-based model checking. In: Hunt, W.A., Somenzi, F. (eds.) CAV 2013. pp. 1–13. Springer, Heidelberg (2003)
McMillan, K.L.: Applications of Craig interpolants in model checking. In: Halbwachs, N., Zuck, L.D. (eds.) Tools and Algorithms for the Construction and Analysis of Systems. pp. 1–12. Springer Berlin Heidelberg, Berlin, Heidelberg (2005)
McMillan, K.L.: An interpolating theorem prover. Theoretical Computer Science 345(1), 101–121 (2005)
McMillan, K.L.: Lazy abstraction with interpolants. In: Computer Aided Verification (CAV ’06). LNCS, vol. 4144, pp. 123–136 (2006)
McMillan, K.L.: Lazy annotation revisited. In: Proc. CAV 2014. LNCS, vol. 8559, pp. 243–259. Springer (2014)
de Moura, L., Bjørner, N.: Z3: An efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. pp. 337–340. Springer, Heidelberg (2008)
Podelski, A., Rybalchenko, A.: Transition invariants. In: Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004. pp. 32–41 (2004)
Podelski, A., Rybalchenko, A.: Transition invariants and transition predicate abstraction for program termination. In: Abdulla, P.A., Leino, K.R.M. (eds.) Tools and Algorithms for the Construction and Analysis of Systems. pp. 3–10. Springer Berlin Heidelberg, Berlin, Heidelberg (2011)
Pudlák, P.: Lower bounds for resolution and cutting plane proofs and monotone computations. Journal of Symbolic Logic 62(3), 981–998 (1997)
Rümmer, P.: Competition report: CHC-COMP-20. Electronic Proceedings in Theoretical Computer Science 320, 197–219 (Aug 2020)
Sharma, R., Dillig, I., Dillig, T., Aiken, A.: Simplifying loop invariant generation using splitter predicates. In: Gopalakrishnan, G., Qadeer, S. (eds.) Computer Aided Verification. pp. 703–719. Springer Berlin Heidelberg, Berlin, Heidelberg (2011)
Vizel, Y., Grumberg, O.: Interpolation-sequence based model checking. In: Proc. FMCAD 2014. pp. 1–8. IEEE (2009)
Zlatkin, I., Fedyukovich, G.: Maximizing branch coverage with constrained horn clauses. In: Fisman, D., Rosu, G. (eds.) Tools and Algorithms for the Construction and Analysis of Systems. Springer Berlin Heidelberg (2022)
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Blicha, M., Fedyukovich, G., Hyvärinen, A.E.J., Sharygina, N. (2022). Transition Power Abstractions for Deep Counterexample Detection. In: Fisman, D., Rosu, G. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2022. Lecture Notes in Computer Science, vol 13243. Springer, Cham. https://doi.org/10.1007/978-3-030-99524-9_29
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