Abstract
Vacuity detection is a method for finding errors in the model-checking process when the specification is found to hold in the model. Most vacuity algorithms are based on checking the effect of applying mutations on the specification. It has been recognized that vacuity results differ in their significance. While in many cases such results are valued as highly informative, there are also cases where a vacuity result is viewed by users as “interesting to know” at the most, or even as meaningless. As of today, no attempt has been made to formally justify this phenomenon.
We suggest and study a framework for ranking vacuity results, based on the probability of the mutated specification to hold on a random computation. For example, two natural mutations of the specification G(req → F ready) are G(¬req) and GF ready. It is agreed that vacuity information about satisfying the first mutation is more alarming than information about satisfying the second. Our methodology formally explains this, as the probability of G(¬req) to hold in a random computation is 0, whereas the probability of GF ready is 1. From a theoretical point of view, we study of the problem of finding the probability of LTL formulas to be satisfied in a random computation and the existence and use of 0/1-laws for fragments of LTL. From a practical point of view, we propose an efficient algorithm for approximating the probability of LTL formulas and provide experimental results demonstrating the usefulness of our approach as well as the suggested algorithm.
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
Preview
Unable to display preview. Download preview PDF.
References
Armoni, R., Fix, L., Flaisher, A., Grumberg, O., Piterman, N., Tiemeyer, A., Vardi, M.Y.: Enhanced vacuity detection in linear temporal logic. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 368–380. Springer, Heidelberg (2003)
Beer, I., Ben-David, S., Eisner, C., Rodeh, Y.: Efficient detection of vacuity in ACTL formulas. Formal Methods in System Design 18(2), 141–162 (2001)
Ben-David, S., Fisman, D., Ruah, S.: Temporal antecedent failure: Refining vacuity. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 492–506. Springer, Heidelberg (2007)
Bustan, D., Flaisher, A., Grumberg, O., Kupferman, O., Vardi, M.Y.: Regular vacuity. In: Borrione, D., Paul, W. (eds.) CHARME 2005. LNCS, vol. 3725, pp. 191–206. Springer, Heidelberg (2005)
Chechik, M., Gheorghiu, M., Gurfinkel, A.: Finding environment guarantees. In: Dwyer, M.B., Lopes, A. (eds.) FASE 2007. LNCS, vol. 4422, pp. 352–367. Springer, Heidelberg (2007)
Chockler, H., Gurfinkel, A., Strichman, O.: Beyond vacuity: Towards the strongest passing formula. In: FMCAD, pp. 1–8 (2008)
Chockler, H., Halpern, J.Y.: Responsibility and blame: a structural-model approach. In: Proc. 19th IJCAI, pp. 147–153 (2003)
Chockler, H., Strichman, O.: Easier and more informative vacuity checks. In: Proc. 5th MEMOCODE, pp. 189–198 (2007)
Clarke, E.M., Grumberg, O., Long, D.: Verification tools for finite-state concurrent systems. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) REX 1993. LNCS, vol. 803, pp. 124–175. Springer, Heidelberg (1994)
Clarke, E.M., Grumberg, O., McMillan, K.L., Zhao, X.: Efficient generation of counterexamples and witnesses in symbolic model checking. In: Proc. 32st DAC, pp. 427–432. IEEE Computer Society (1995)
Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. J. ACM 42, 857–907 (1995)
Dwyer, M.B., Avrunin, G.S., Corbett, J.C.: Property pattern mappings for LTL, http://patterns.projects.cis.ksu.edu/documentation/patterns/ltl.shtml
Dwyer, M.B., Avrunin, G.S., Corbett, J.C.: Property specification patterns for finite-state verification. In: FMSP, pp. 7–15 (1998)
Fagin, R.: Probabilities in finite models. JSL 41(1), 50–58 (1976)
Fisman, D., Kupferman, O., Sheinvald-Faragy, S., Vardi, M.Y.: A framework for inherent vacuity. In: Chockler, H., Hu, A.J. (eds.) HVC 2008. LNCS, vol. 5394, pp. 7–22. Springer, Heidelberg (2009)
Glebskii, Y.V., Kogan, D.I., Liogonkii, M.I., Talanov, V.A.: Range and degree of realizability of formulas in the restricted predicate calculus. Kibernetika 2, 17–28 (1969)
Gurfinkel, A., Chechik, M.: Extending extended vacuity. In: Hu, A.J., Martin, A.K. (eds.) FMCAD 2004. LNCS, vol. 3312, pp. 306–321. Springer, Heidelberg (2004)
Gurfinkel, A., Chechik, M.: How vacuous is vacuous? In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 451–466. Springer, Heidelberg (2004)
Kupferman, O.: Sanity checks in formal verification. In: Baier, C., Hermanns, H. (eds.) CONCUR 2006. LNCS, vol. 4137, pp. 37–51. Springer, Heidelberg (2006)
Kupferman, O., Li, W., Seshia, S.A.: A theory of mutations with applications to vacuity, coverage, and fault tolerance. In: FMCAD 2008, pp. 1–9 (2008)
Kupferman, O., Vardi, M.Y.: Vacuity detection in temporal model checking. STTT 4(2), 224–233 (2003)
Pnueli, A.: The temporal logic of programs. In: Proc. 18th FOCS, pp. 46–57 (1977)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Ben-David, S., Kupferman, O. (2013). A Framework for Ranking Vacuity Results. In: Van Hung, D., Ogawa, M. (eds) Automated Technology for Verification and Analysis. Lecture Notes in Computer Science, vol 8172. Springer, Cham. https://doi.org/10.1007/978-3-319-02444-8_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-02444-8_12
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02443-1
Online ISBN: 978-3-319-02444-8
eBook Packages: Computer ScienceComputer Science (R0)