Abstract
This paper evaluates different algorithms for existential Boolean quantifier elimination in the area of automotive configuration. We compare approaches based on model enumeration, on resolution, on dependency sequents, on substitution, and on knowledge compilation with projection. We describe two real-life applications: model counting on a set of customer-relevant options and projection of BOM (bill of materials) constraints. Our work includes an implementation of the presented techniques on top of state-of-the-art tools. We evaluate the different approaches on real production data from our collaboration with BMW.
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
Sabin, D., Weigel, R.: Product configuration frameworks-a survey. IEEE Intelligent Systems 13, 42–49 (1998)
Astesana, J.M., Bossu, Y., Cosserat, L., Fargier, H.: Constraint-based modeling and exploitation of a vehicle range at Renault’s: Requirement analysis and complexity study. In: Proceedings of the ConfWS 2010, pp. 33–39 (2010)
Küchlin, W., Sinz, C.: Proving consistency assertions for automotive product data management. Journal of Automated Reasoning 24, 145–163 (2000)
Seidl, A.M., Sturm, T.: Boolean quantification in a first-order context. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds.) Proceedings of the CASC 2003, pp. 329–345. Institut für Informatik, TU München (2003)
Benedetti, M., Mangassarian, H.: QBF-based formal verification: Experience and perspectives. JSAT 5, 133–191 (2008)
Sturm, T., Zengler, C.: Parametric quantified SAT solving. In: Proceedings of the ISSAC 2010. ACM, New York (2010)
McMillan, K.L.: Symbolic Model Checking. Kluwer Academic Publishers, Norwell (1993)
McMillan, K.L.: Applying SAT methods in unbounded symbolic model checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, p. 250. Springer, Heidelberg (2002)
Narodytska, N., Walsh, T.: Constraint and variable ordering heuristics for compiling configuration problems. In: Proceedings of the IJCAI 2007, pp. 149–154. Morgan Kaufmann Publishers Inc., San Francisco (2007)
Matthes, B., Zengler, C., Küchlin, W.: An improved constraint ordering heuristics for compiling configuration problems. In: Mayer, W., Albert, P. (eds.) Proceedings of the ConfWS, pp. 36–40 (2012)
Darwiche, A.: Decomposable negation normal form. Journal of the ACM 48, 608–647 (2001)
Grumberg, O., Schuster, A., Yadgar, A.: Memory efficient all-solutions SAT solver and its application for reachability analysis. In: Hu, A.J., Martin, A.K. (eds.) FMCAD 2004. LNCS, vol. 3312, pp. 275–289. Springer, Heidelberg (2004)
Gebser, M., Kaufmann, B., Schaub, T.: Solution enumeration for projected boolean search problems. In: van Hoeve, W.-J., Hooker, J.N. (eds.) CPAIOR 2009. LNCS, vol. 5547, pp. 71–86. Springer, Heidelberg (2009)
Brauer, J., King, A., Kriener, J.: Existential quantification as incremental sat. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 191–207. Springer, Heidelberg (2011)
Davis, M., Putnam, H.: A computing procedure for quantification theory. Journal of the ACM 7, 201–215 (1960)
Biere, A.: Resolve and expand. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 59–70. Springer, Heidelberg (2005)
Goldberg, E., Manolios, P.: Quantifier elimination by dependency sequents. In: Proceedings of the FMCAD 2012, pp. 34–43. IEEE Computer Society (2012)
Kübler, A., Zengler, C., Küchlin, W.: Model counting in product configuration. In: Proceedings of the LoCoCo 2010. EPTCS, vol. 29, pp. 44–53 (2010)
Ayari, A., Basin, D.: Qubos: Deciding quantified Boolean logic using propositional satisfiability solvers. In: Aagaard, M.D., O’Leary, J.W. (eds.) FMCAD 2002. LNCS, vol. 2517, pp. 187–201. Springer, Heidelberg (2002)
Darwiche, A.: New advances in compiling CNF to decomposable negational normal form. In: Proceedings of the ECAI 2004. IOS Press (2004)
Zengler, C., Kübler, A., Küchlin, W.: New approaches to boolean quantifier elimination. ACM Communications in Computer Algebra 45, 139–140 (2011)
Darwiche, A., Hopkins, M.: Using recursive decomposition to construct elimination orders, jointrees, and dtrees. In: Benferhat, S., Besnard, P. (eds.) ECSQARU 2001. LNCS (LNAI), vol. 2143, pp. 180–191. Springer, Heidelberg (2001)
Pipatsrisawat, K., Darwiche, A.: New compilation languages based on structured decomposability. In: Proceedings of the AAAI 2008, pp. 517–522. AAAI Press (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zengler, C., Küchlin, W. (2013). Boolean Quantifier Elimination for Automotive Configuration – A Case Study. In: Pecheur, C., Dierkes, M. (eds) Formal Methods for Industrial Critical Systems. FMICS 2013. Lecture Notes in Computer Science, vol 8187. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41010-9_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-41010-9_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-41009-3
Online ISBN: 978-3-642-41010-9
eBook Packages: Computer ScienceComputer Science (R0)