Abstract
We present a framework for fully automated compositional verification of μ-calculus specifications over multi-valued systems, based on multi-valued abstraction and refinement.
Multi-valued models are widely used in many applications of model checking. They enable a more precise modeling of systems by distinguishing several levels of uncertainty and inconsistency. Successful verification tools such as STE (for hardware) and YASM (for software) are based on multi-valued models.
Our compositional approach model checks individual components of a system. Only if all individual checks return indefinite values, the parts of the components which are responsible for these values, are composed and checked. Thus the construction of the full system is avoided. If the latter check is still indefinite, then a refinement is needed.
We formalize our framework based on bilattices, consisting of a truth lattice and an information lattice. Formulas interpreted over a multi-valued model are evaluated w.r.t. to the truth lattice. On the other hand, refinement is now aimed at increasing the information level of model details, thus also increasing the information level of the model checking result. Based on the two lattices, we suggest how multi-valued models should be composed, checked, and refined.
An extended version including full proofs is published as a technical report in [19].
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Ball, T., Kupferman, O., Yorsh, G.: Abstraction for falsification. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 67–81. Springer, Heidelberg (2005)
Belnap, N.D.: A useful four-valued logic. In: Modern uses of multiple valued logics (1977)
Bruns, G., Godefroid, P.: Model checking partial state spaces with 3-valued temporal logics. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 274–287. Springer, Heidelberg (1999)
Bruns, G., Godefroid, P.: Model checking with multi-valued logics. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 281–293. Springer, Heidelberg (2004)
Bruns, G., Godefroid, P.: Temporal logic query checking. In: LICS 2001 (2001)
Chan, W.: Temporal-logic queries. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 450–463. Springer, Heidelberg (2000)
Chechik, M., Devereux, B., Easterbrook, S.M., Gurfinkel, A.: Multi-valued symbolic model-checking. In: ACM Transactions on Software Engineering and Methodology, vol. 12 (2003)
Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (1999)
Dams, D., Gerth, R., Grumberg, O.: Abstract interpretation of reactive systems. ACM Trans. Program. Lang. Syst. 19(2) (1997)
Easterbrook, S.M., Chechik, M.: A framework for multi-valued reasoning over inconsistent viewpoints. In: ICSE 2001 (2001)
Fitting, M.: Bilattices are nice things. In: Self-Reference (2002)
Godefroid, P., Jagadeesan, R.: Automatic abstraction using generalized model checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, p. 137. Springer, Heidelberg (2002)
Grumberg, O., Lange, M., Leucker, M., Shoham, S.: When not losing is better than winning: Abstraction and refinement for the full μ-calculus. Information and Computation 205(8) (2007)
Gurfinkel, A., Chechik, M.: Why waste a perfectly good abstraction? In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 212–226. Springer, Heidelberg (2006)
Gurfinkel, A., Wei, O., Chechik, M.: Systematic construction of abstractions for model-checking. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 381–397. Springer, Heidelberg (2006)
Huth, M., Pradhan, S.: Lifting assertion and consistency checkers from single to multiple viewpoints. In: TR 2002/11, Dept. of Computing. Imperial College, London (2002)
Jain, H., Kroening, D., Sharygina, N., Clarke, E.M.: Word level predicate abstraction and refinement for verifying RTL Verilog. In: DAC 2005 (2005)
Kupferman, O., Lustig, Y.: Latticed simulation relations and games. In: Namjoshi, K.S., Yoneda, T., Higashino, T., Okamura, Y. (eds.) ATVA 2007. LNCS, vol. 4762, pp. 316–330. Springer, Heidelberg (2007)
Meller, Y., Grumberg, O., Shoham, S.: A framework for compositional verification of multi-valued systems via abstraction-refinement. In: TR CS-2009-14, Dept. of Computer Science. Technion – Israel Institute of Technology (2009)
Seger, C.-J.H., Bryant, R.E.: Formal verification by symbolic evaluation of partially-ordered trajectories. Formal Methods in System Design 6(2) (1995)
Shoham, S., Grumberg, O.: Compositional verification and 3-valued abstractions join forces. In: Riis Nielson, H., Filé, G. (eds.) SAS 2007. LNCS, vol. 4634, pp. 69–86. Springer, Heidelberg (2007)
Shoham, S., Grumberg, O.: Multi-valued model checking games. In: Peled, D.A., Tsay, Y.-K. (eds.) ATVA 2005. LNCS, vol. 3707, pp. 354–369. Springer, Heidelberg (2005)
Tarski, A.: A lattice-theoretical fixpoint theorem and its applications. Pacific J. Math. 5 (1955)
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Meller, Y., Grumberg, O., Shoham, S. (2009). A Framework for Compositional Verification of Multi-valued Systems via Abstraction-Refinement. In: Liu, Z., Ravn, A.P. (eds) Automated Technology for Verification and Analysis. ATVA 2009. Lecture Notes in Computer Science, vol 5799. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04761-9_21
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