Abstract
Smooth decomposable negation normal form (s-DNNF) circuits are a compact form of representing many Boolean functions, that permit linear time satisfiability checking. Given a constraint defined by an s-DNNF circuit, we can create a propagator for the constraint by decomposing the circuit using a Tseitin transformation. But this introduces many additional Boolean variables, and hides the structure of the original s-DNNF. In this paper we show how we can build a propagator that works on the s-DNNF circuit directly, and can be integrated into a lazy-clause generation-based constraint solver. We show that the resulting propagator can efficiently solve problems where s-DNNF circuits are the natural representation of the constraints of the problem, outperforming the decomposition based approach.
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
Cheng, K.C.K., Yap, R.H.C.: Maintaining Generalized Arc Consistency on Ad Hoc r-Ary Constraints. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 509–523. Springer, Heidelberg (2008)
Gange, G., Stuckey, P., Lagoon, V.: Fast set bounds propagation using a BDD-SAT hybrid. Journal of Artificial Intelligence Research 38, 307–338 (2010)
Gange, G., Stuckey, P.J., Szymanek, R.: MDD propagators with explanation. Constraints 16(4), 407–429 (2011)
Pesant, G.: A Regular Language Membership Constraint for Finite Sequences of Variables. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 482–495. Springer, Heidelberg (2004)
Darwiche, A.: Sdd: A new canonical representation of propositional knowledge bases. In: IJCAI, pp. 819–826 (2011)
Tseitin, G.: On the complexity of derivation in propositional calculus. Studies in Constructive Mathematics and Mathematical Logic, part 2, pp. 115–125 (1968)
Schulte, C., Stuckey, P.: Efficient constraint propagation engines. ACM Transactions on Programming Languages and Systems 31(1), Article No. 2 (2008)
Ohrimenko, O., Stuckey, P., Codish, M.: Propagation via lazy clause generation. Constraints 14(3), 357–391 (2009)
Fargier, H., Marquis, P.: On valued negation normal form formulas. In: IJCAI, pp. 360–365 (2007)
Darwiche, A., Marquis, P.: A knowledge compilation map. Journal of Artificial Intelligence Research 17, 229–264 (2002)
Quimper, C., Walsh, T.: Global Grammar Constraints. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 751–755. Springer, Heidelberg (2006)
Jung, J.C., Barahona, P., Katsirelos, G., Walsh, T.: Two encodings of DNNF theories. In: ECAI Workshop on Inference Methods Based on Graphical Structures of Knowledge (2008)
Hawkins, P., Stuckey, P.J.: A Hybrid BDD and SAT Finite Domain Constraint Solver. In: Van Hentenryck, P. (ed.) PADL 2006. LNCS, vol. 3819, pp. 103–117. Springer, Heidelberg (2005)
Subbarayan, S.: Efficient Reasoning for Nogoods in Constraint Solvers with BDDs. In: Hudak, P., Warren, D.S. (eds.) PADL 2008. LNCS, vol. 4902, pp. 53–67. Springer, Heidelberg (2008)
Demassey, S., Pesant, G., Rousseau, L.M.: A cost-regular based hybrid column generation approach. Constraints 11(4), 315–333 (2006)
Abío, I., Nieuwenhuis, R., Oliveras, A., Rodríguez-Carbonell, E.: BDDs for Pseudo-Boolean Constraints – Revisited. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 61–75. Springer, Heidelberg (2011)
Katsirelos, G., Narodytska, N., Walsh, T.: Reformulating global grammar constraints. Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 132–147 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gange, G., Stuckey, P.J. (2012). Explaining Propagators for s-DNNF Circuits. In: Beldiceanu, N., Jussien, N., Pinson, É. (eds) Integration of AI and OR Techniques in Contraint Programming for Combinatorial Optimzation Problems. CPAIOR 2012. Lecture Notes in Computer Science, vol 7298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29828-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-29828-8_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29827-1
Online ISBN: 978-3-642-29828-8
eBook Packages: Computer ScienceComputer Science (R0)