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Satisfiability Checking: Theory and Applications

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Software Engineering and Formal Methods (SEFM 2016)

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Abstract

Satisfiability checking aims to develop algorithms and tools for checking the satisfiability of existentially quantified logical formulas. Besides powerful SAT solvers for solving propositional logic formulas, sophisticated SAT-modulo-theories (SMT) solvers are available for a wide range of theories, and are applied as black-box engines for many techniques in different areas. In this paper we give a short introduction to the theoretical foundations of satisfiability checking, mention some of the most popular tools, and discuss the successful embedding of SMT solvers in different technologies.

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References

  1. Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking. In: Proceedings of ISSAC 2015, pp. 1–6. ACM (2015)

    Google Scholar 

  2. Ansótegui, C., Bofill, M., Palahı, M., Suy, J., Villaret, M.: Satisfiability modulo theories: An efficient approach for the resource-constrained project scheduling problem. In: Proceedings of SARA 2011, pp. 2–9. AAAI (2011)

    Google Scholar 

  3. Avalanche.: Dynamic program analysis tool. http://www.ispras.ru/en/technologies/avalanche_dynamic_program_analysis_tool/

  4. Bae, K., Ölveczky, P.C., Kong, S., Gao, S., Clarke, E.M.: SMT-based analysis of virtually synchronous distributed hybrid systems. In: Proceedings of HSCC 2016 (2016). (to appear)

    Google Scholar 

  5. Ball, T., Bounimova, E., Levin, V., De Moura, L.: Efficient evaluation of pointer predicates with Z3 SMT solver in SLAM2. Technical report, Microsoft Research (2010)

    Google Scholar 

  6. Barrett, C., Conway, C.L., Deters, M., Hadarean, L., Jovanović, D., King, T., Reynolds, A., Tinelli, C.: CVC4. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 171–177. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  7. Barrett, C.W., de Moura, L., Stump, A.: SMT-COMP: satisfiability modulo theories competition. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 20–23. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  8. Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB) (2016). www.SMT-LIB.org

  9. Barrett, C., Sebastiani, R., Seshia, S.A., Tinelli, C.: Satisfiability modulo theories. In: Biere, A., Heule, M.J.H., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability, Chap. 26. Frontiers in Artificial Intelligence and Applications, vol. 185, pp. 825–885. IOS Press, Amsterdam (2009)

    Google Scholar 

  10. Biere, A., Biere, A., Heule, M., van Maaren, H., Walsh, T.: Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press, Amsterdam (2009)

    MATH  Google Scholar 

  11. Biere, A., Cimatti, A., Clarke, E., Zhu, Y.: Symbolic model checking without BDDs. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  12. Bjørner, N., Jayaraman, K.: Checking cloud contracts in microsoft azure. In: Natarajan, R., Barua, G., Patra, M.R. (eds.) ICDCIT 2015. LNCS, vol. 8956, pp. 21–32. Springer, Heidelberg (2015)

    Google Scholar 

  13. Bjørner, N., Phan, A.-D., Fleckenstein, L.: \(\nu \) Z - an optimizing SMT solver. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 194–199. Springer, Heidelberg (2015)

    Google Scholar 

  14. Bofill, M., Coll, J., Suy, J., Villaret, M.: A system for generation and visualization of resource-constrained projects. In: Proceedings of CCIA 2014. Frontiers in Artificial Intelligence and Applications, vol. 269, pp. 237–246. IOS Press (2014)

    Google Scholar 

  15. Boogie.: An intermediate verification language. http://research.microsoft.com/en-us/projects/boogie/

  16. Bouton, Thomas, de Oliveira, D.C.B., Déharbe, D., Fontaine, P.: \({\sf { veriT}}\): an open, trustable and efficient SMT-solver. In: Schmidt, Renate A. (ed.) CADE-22. LNCS, vol. 5663, pp. 151–156. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  17. Bradley, A.R.: SAT-based model checking without unrolling. In: Schmidt, D., Jhala, R. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 70–87. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  18. Bruttomesso, R., Pek, E., Sharygina, N., Tsitovich, A.: The OpenSMT solver. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 150–153. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  19. Cadar, C., Dunbar, D., Engler, D.: KLEE: Unassisted and automatic generation of high-coverage tests for complex systems programs. In: Proceedings of OSDI 2008, pp. 209–224. USENIX Association (2008)

    Google Scholar 

  20. Catan, M., et al.: Aeolus: mastering the complexity of cloud application deployment. In: Lau, K.-K., Lamersdorf, W., Pimentel, E. (eds.) ESOCC 2013. LNCS, vol. 8135, pp. 1–3. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  21. Christ, J., Hoenicke, J., Nutz, A.: SMTInterpol: an interpolating SMT solver. In: Donaldson, A., Parker, D. (eds.) SPIN 2012. LNCS, vol. 7385, pp. 248–254. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  22. Cimatti, A., Griggio, A., Schaafsma, B.J., Sebastiani, R.: The MathSAT5 SMT solver. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013 (ETAPS 2013). LNCS, vol. 7795, pp. 93–107. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  23. Cimatti, A., Mover, S., Tonetta, S.: A quantifier-free SMT encoding of non-linear hybrid automata. In: Proceedings of FMCAD 2012, pp. 187–195. IEEE (2012)

    Google Scholar 

  24. Collins, G.E.: Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In: Brakhage, H. (ed.) Automata Theory and Formal Languages. LNCS, vol. 33, pp. 134–183. Springer, Heidelberg (1975)

    Google Scholar 

  25. Conchon, S., Iguernelala, M., Mebsout, A.: A collaborative framework for non-linear integer arithmetic reasoning in Alt-Ergo. In: Proceedings of SYNASC 2013, pp. 161–168. IEEE (2013)

    Google Scholar 

  26. Corzilius, F., Kremer, G., Junges, S., Schupp, S., Ábrahám, E.: SMT-RAT: an open source C++ toolbox for strategic and parallel SMT solving. In: Heule, M., et al. (eds.) SAT 2015. LNCS, vol. 9340, pp. 360–368. Springer, Heidelberg (2015). doi:10.1007/978-3-319-24318-4_26

    Chapter  Google Scholar 

  27. Craciunas, S.S., Oliver, R.S.: SMT-based task- and network-level static schedule generation for time-triggered networked systems. In: Proceedings of RTNS 2014, p. 45. ACM (2014)

    Google Scholar 

  28. Dantzig, G.B.: Linear Programming and Extensions. Princeton University Press, Princeton (1963)

    MATH  Google Scholar 

  29. Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Commun. ACM 5(7), 394–397 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  30. Davis, M., Putnam, H.: A computing procedure for quantification theory. J. ACM 7(3), 201–215 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  31. Déharbe, D., Fontaine, P., Guyot, Y., Voisin, L.: Integrating SMT solvers in Rodin. Sci. Comput. Program. 94(P2), 130–143 (2014)

    Article  Google Scholar 

  32. Dutertre, B.: Yices 2.2. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 737–744. Springer, Heidelberg (2014)

    Google Scholar 

  33. Eggers, A., Ramdani, N., Nedialkov, N.S., Fränzle, M.: Improving the SAT modulo ODE approach to hybrid systems analysis by combining different enclosure methods. Softw. Syst. Model. 14(1), 121–148 (2012)

    Article  MATH  Google Scholar 

  34. Fränzle, M., Herde, C., Teige, T., Ratschan, S., Schubert, T.: Efficient solving of large non-linear arithmetic constraint systems with complex Boolean structure. J. Satisf. Boolean Model. Comput. 1(3–4), 209–236 (2007)

    MATH  Google Scholar 

  35. 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)

    Chapter  Google Scholar 

  36. Gao, S., Ganai, M., Ivančić, F., Gupta, A., Sankaranarayanan, S., Clarke, E.M.: Integrating ICP and LRA solvers for deciding nonlinear real arithmetic problems. In: Proceedings of FMCAD 2010, pp. 81–90. IEEE (2010)

    Google Scholar 

  37. Giesl, J., et al.: Proving termination of programs automatically with \({\sf { AProVE}}\). In: Demri, S., Kapur, D., Weidenbach, C. (eds.) IJCAR 2014. LNCS, vol. 8562, pp. 184–191. Springer, Heidelberg (2014)

    Google Scholar 

  38. Hallin, M.: SMT-Based Reasoning and Planning in TAL. Master’s thesis, Linköping University (2010)

    Google Scholar 

  39. Herbort, S., Ratz, D.: Improving the efficiency of a nonlinear-system-solver using a componentwise Newton method. Technical report 2/1997, Inst. für Angewandte Mathematik, University of Karlsruhe (1997)

    Google Scholar 

  40. Jayaraman, K., Bjrner, N., Outhred, G., Kaufman, C.: Automated analysis and debugging of network connectivity policies. Technical report MSR-TR-2014-102, Microsoft Research (2014). http://research.microsoft.com/apps/pubs/default.aspx?id=225826

  41. Jovanović, D., de Moura, L.: Solving non-linear arithmetic. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS, vol. 7364, pp. 339–354. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  42. Kahsai, T., Tinelli, C.: PKIND: A parallel \(k\)-induction based model checker. arXiv preprint (2011). arXiv:1111.0372

  43. Khanh, T.V., Vu, X., Ogawa, M.: raSAT: SMT for polynomial inequality. In: Proceedings of SMT 2014, p. 67 (2014)

    Google Scholar 

  44. Kong, S., Gao, S., Chen, W., Clarke, E.: \({\sf dReach:} \delta \)-reachability analysis for hybrid systems. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 200–205. Springer, Heidelberg (2015)

    Google Scholar 

  45. Korp, M., Sternagel, C., Zankl, H., Middeldorp, A.: Tyrolean termination tool 2. In: Treinen, R. (ed.) RTA 2009. LNCS, vol. 5595, pp. 295–304. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  46. Kroening, D., Strichman, O.: Decision Procedures: An Algorithmic Point of View. Springer, New York (2008)

    MATH  Google Scholar 

  47. Kroening, D., Tautschnig, M.: CBMC – C bounded model checker. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014 (ETAPS). LNCS, vol. 8413, pp. 389–391. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  48. Lange, T., Neuhäußer, M.R., Noll, T.: IC3 software model checking on control flow automata. In: Proceedings of FMCAD 2015, pp. 97–104. IEEE (2015)

    Google Scholar 

  49. Li, Y., Albarghouthi, A., Kincaid, Z., Gurfinkel, A., Chechik, M.: Symbolic optimization with SMT solvers. In: Proceedings of POPL 2014, pp. 607–618. ACM (2014)

    Google Scholar 

  50. Marques-silva, J.P., Sakallah, K.A.: Grasp: a search algorithm for propositional satisfiability. IEEE Trans. Comput. 48, 506–521 (1999)

    Article  MathSciNet  Google Scholar 

  51. 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)

    Chapter  Google Scholar 

  52. de Moura, L., Passmore, G.O.: The strategy challenge in SMT solving. In: Bonacina, M.P., Stickel, M.E. (eds.) Automated Reasoning and Mathematics. LNCS, vol. 7788, pp. 15–44. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  53. Nedunuri, S., Prabhu, S., Moll, M., Chaudhuri, S., Kavraki, L.E.: SMT-based synthesis of integrated task and motion plans from plan outlines. In: Proceedings of ICRA 2014, pp. 655–662. IEEE (2014)

    Google Scholar 

  54. Nelson, G., Oppen, D.C.: Simplification by cooperating decision procedures. ACM Trans. Program. Lang. Syst. 1(2), 245–257 (1979)

    Article  MATH  Google Scholar 

  55. Niemetz, A., Preiner, M., Biere, A.: Boolector 2.0. J. Satisf. Boolean Model. Comput. 9, 53–58 (2015)

    Google Scholar 

  56. Peleska, J., Vorobev, E., Lapschies, F.: Automated test case generation with SMT-solving and abstract interpretation. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 298–312. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  57. Phothilimthana, P.M., Thakur, A., Bodik, R., Dhurjati, D.: GreenThumb: Superoptimizer construction framework. In: Proceedings of CCC 2016, pp. 261–262. ACM (2016)

    Google Scholar 

  58. Pike, L.: Modeling time-triggered protocols and verifying their real-time schedules. In: Proceedings of FMCAD 2007, pp. 231–238. IEEE (2007)

    Google Scholar 

  59. Rintanen, J.: Discretization of temporal models with application to planning with SMT. In: Proceedings of AAAI 2015, pp. 3349–3355. AAAI (2015)

    Google Scholar 

  60. Symbolic analysis laboratory. http://sal.csl.sri.com/introduction.shtml

  61. Scala, E., Ramirez, M., Haslum, P., Thiebaux, S.: Numeric planning with disjunctive global constraints via SMT. In: Proceedings of ICASP 2016 (2016, to appear)

    Google Scholar 

  62. Scheibler, K., Kupferschmid, S., Becker, B.: Recent improvements in the SMT solver iSAT. In: Proceedings of MBMV 2013, pp. 231–241. Institut für Angewandte Mikroelektronik und Datentechnik, Fakultät für Informatik und Elektrotechnik, Universität Rostock (2013)

    Google Scholar 

  63. Sebastiani, R., Trentin, P.: OptiMathSAT: a tool for optimization modulo theories. In: Kroening, D., Păsăreanu, C.S. (eds.) CAV 2015. LNCS, vol. 9206, pp. 447–454. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  64. SMT-COMP 2015 result summary (2015). http://smtcomp.sourceforge.net/2015/results-summary.shtml

  65. Souper. http://github.com/google/souper

  66. Tiwari, A., Gascón, A., Dutertre, B.: Program synthesis using dual interpretation. In: Felty, A., Middeldorp, A. (eds.) CADE-25. Lecture Notes in Computer Science, vol. 9195, pp. 482–497. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  67. Tseitin, G.S.: On the complexity of derivation in propositional calculus. In: Siekmann, J.H., Wrightson, G. (eds.) Automation of Reasoning, pp. 466–483. Springer, New York (1983)

    Chapter  Google Scholar 

  68. Weispfenning, V.: A new approach to quantifier elimination for real algebra. In: Caviness, B.F., Johnson, J.R. (eds.) Quantifier Elimination and Cylindrical Algebraic Decomposition. Texts and Monographs in Symbolic Computation, pp. 376–392. Springer, NEw York (1998)

    Chapter  Google Scholar 

  69. Weispfenning, V.: Quantifier elimination for real algebra - the quadratic case and beyond. Appl. Algebra Eng. Commun. Comput. 8(2), 85–101 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  70. Wintersteiger, C.M., Hamadi, Y., de Moura, L.: A concurrent portfolio approach to SMT solving. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 715–720. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  71. Yamada, A., Kusakari, K., Sakabe, T.: Nagoya termination tool. In: Dowek, G. (ed.) RTA-TLCA 2014. LNCS, vol. 8560, pp. 466–475. Springer, Heidelberg (2014)

    Google Scholar 

  72. Yuan, M., He, X., Gu, Z.: Hardware/software partitioning and static task scheduling on runtime reconfigurable FPGAs using an SMT solver. In: Proceedings of RTAS 2008, pp. 295–304. IEEE (2008)

    Google Scholar 

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  1. RWTH Aachen University, Aachen, Germany

    Erika Ábrahám & Gereon Kremer

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  1. Erika Ábrahám
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  2. Gereon Kremer
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Correspondence to Erika Ábrahám .

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  1. IMT - School for Advanced Studies, Lucca, Italy

    Rocco De Nicola

  2. Institute of Computer Languages, TU Wien, Wien, Austria

    Eva Kühn

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Ábrahám, E., Kremer, G. (2016). Satisfiability Checking: Theory and Applications. In: De Nicola, R., Kühn, E. (eds) Software Engineering and Formal Methods. SEFM 2016. Lecture Notes in Computer Science(), vol 9763. Springer, Cham. https://doi.org/10.1007/978-3-319-41591-8_2

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