Abstract
The method of Invisible Invariants was conceived to verify properties of parameterized systems, for any instantiation, in one fell swoop. Given a deductive proof rule for the desired property, the method calls for two steps: (1) An heuristic to generate the hypothesis of the proof rule, and (2) a method to validate the premises of the proof rule once an hypothesis is generated.
At the time of its conception, the method was carried out by model checkers based on BDDs, and both steps were performed without ever having to explicitly generate the hypotheses, which rendered them “Invisible”. Moreover, initially the method was applied to generate invariants, but shortly after its introduction, it was used to generate other types of hypotheses. Nowadays, the method can be applied without BDDs, which renders Invisible Invariants to be neither invisible nor invariants.
In this paper we attempt to shed light on the fundamental ideas of the method and to argue for its applicability for a large class of infinite-state systems.
The work of the first co-author was partially funded by NSF award CCF-1563393.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
That is, we justify induction by appeal to induction, a method called into question by David Hume [7].
- 2.
This process is akin to Alice’s rule in the “Mock Turtle’s Story”: Take care of the sense, and the sounds will take care of themselves.
References
Pnueli, A., Zuck, L.: Parameterized verification by probabilistic abstraction. In: Gordon, A.D. (ed.) FoSSaCS 2003. LNCS, vol. 2620, pp. 87–102. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36576-1_6
Balaban, I., Pnueli, A., Sa’ar, Y., Zuck, L.D.: Verification of multi-linked heaps. J. Comput. Syst. Sci. 78(3), 853–876 (2012)
Balaban, I., Pnueli, A., Zuck, L.D.: Shape analysis by predicate abstraction. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 164–180. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30579-8_12
Balaban, I., Pnueli, A., Zuck, L.D.: Shape analysis of single-parent heaps. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol. 4349, pp. 91–105. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-69738-1_7
Fang, Y., McMillan, K.L., Pnueli, A., Zuck, L.D.: Liveness by invisible invariants. In: Najm, E., Pradat-Peyre, J.-F., Donzeau-Gouge, V.V. (eds.) FORTE 2006. LNCS, vol. 4229, pp. 356–371. Springer, Heidelberg (2006). https://doi.org/10.1007/11888116_26
Goodman, N.: Fact Fiction and Forecast, 4th edn. Harvard University Press, Cambridge (1983)
Hume, D.: Treatise of Human Nature. Clarendon Press, Oxford (1888). Edited by L. A Selby Bigge. Originally published 1739–1740
Lahiri, S.K.: Ubounded system verification using decision procedure and predicate abstraction. Ph.D. thesis, Carnegie Mellon University (2004)
Lamport, L.: Proving the correctness of multiprocess programs. IEEE Trans. Softw. Eng. SE-3, 2:125–143, 3 (1977)
Manna, Z., Pnueli, A.: Temporal Verification of Reactive Systems: Safety. Springer, New York (1995). https://doi.org/10.1007/978-1-4612-4222-2
Mitchell, T.M.: The need for biases in learning generalizations, Technical report (1980)
Owicki, S., Gries, D.: Verifying properties of parallel programs: an axiomatic approach. Commun. ACM 19(5), 279–285, 5 (1976)
Pnueli, A., Ruah, S., Zuck, L.: Automatic deductive verification with invisible invariants. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 82–97. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45319-9_7
Pnueli, A., Zuck, L.D.: Probabilistic verification by tableaux. In: Proceedings of the Symposium on Logic in Computer Science (LICS 1986), Cambridge, Massachusetts, USA, 16–18 June 1986, pp. 322–331 (1986)
Reps, T., Sagiv, M., Yorsh, G.: Symbolic implementation of the best transformer. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 252–266. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24622-0_21
Russell, S.J., Norvig, P.: Artificial Intelligence: A Modern Approach, 3rd edn. Pearson Education Limited, London (2014)
Zuck, L., Pnueli, A., Kesten, Y.: Automatic verification of probabilistic free choice. In: Cortesi, A. (ed.) VMCAI 2002. LNCS, vol. 2294, pp. 208–224. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-47813-2_15
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Zuck, L.D., McMillan, K.L. (2019). Invisible Invariants Are Neither. In: Bartocci, E., Cleaveland, R., Grosu, R., Sokolsky, O. (eds) From Reactive Systems to Cyber-Physical Systems. Lecture Notes in Computer Science(), vol 11500. Springer, Cham. https://doi.org/10.1007/978-3-030-31514-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-31514-6_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-31513-9
Online ISBN: 978-3-030-31514-6
eBook Packages: Computer ScienceComputer Science (R0)