Abstract
Specifications of constraint problems can be considered logical formulae. As a consequence, it is possible to infer their properties by means of automated reasoning tools, with the goal of automatically synthesizing transformations that can make the solving process more efficient. The purpose of this paper is to link two important technologies: automated theorem proving and constraint programming. We report the results on using ATP technology for checking existence of symmetries, checking whether a given formula breaks a symmetry, and checking existence of functional dependencies in a specification. The output of the reasoning phase is a transformed constraint program, consisting in a reformulated specification and, possibly a search strategy. We show our techniques on problems such as Graph coloring, Sailco inventory and Protein folding.
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.
Similar content being viewed by others
References
Cadoli, M., Mancini, T.: Detecting and breaking symmetries on specifications. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 165–181. Springer, Heidelberg (2003)
Cadoli, M., Mancini, T.: Automated reformulation of specifications by safe delay of constraints. In: Proc. of KR 2004. AAAI Press/The MIT Press (2004)
Cadoli, M., Mancini, T.: Exploiting functional dependencies in declarative problem specifications. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 628–640. Springer, Heidelberg (2004)
Cadoli, M., Schaerf, A.: Compiling problem specifications into SAT. Artif. Intell. 162, 89–120 (2005)
Castillo, E., Conejo, A.J., Pedregal, P., Garcia, R., Alguacil, N.: Building and Solving Mathematical Programming Models in Engineering and Science. John Wiley & Sons, Chichester (2001)
Dechter, R.: Constraint Networks (Survey). John Wiley & Sons, Chichester (1992)
Fagin, R.: Generalized first-order spectra and polynomial-time recognizable sets. In: Karp, R.M. (ed.) Complexity of Computation, pp. 43–74. Amer. Math. Soc., Providence (1974)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Co., New York (1979)
Giunchiglia, E., Sebastiani, R.: Applying the Davis-Putnam procedure to non-clausal formulas. In: Proc. of AI*IA 1999, Springer, Heidelberg (2000)
Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S., Scarcello, F.: The DLV System for Knowledge Representation and Reasoning. ACM Trans. on Comp. Logic (to appear)
Li, C.M.: Integrating equivalency reasoning into Davis-Putnam procedure. In: Proc. of AAAI 2000, AAAI Press/The MIT Press (2000)
Mancini, T., Cadoli, M.: Detecting and breaking symmetries by reasoning on problem specifications. In: Zucker, J.-D., Saitta, L. (eds.) SARA 2005. LNCS (LNAI), vol. 3607, pp. 165–181. Springer, Heidelberg (2005)
McCune, W.: MACE 2.0 reference manual and guide. Tech. Rep. ANL/MCS-TM-249, Argonne Nat. Lab., Math. and Comp. Sci. Div. (2001), Available at, http://www-unix.mcs.anl.gov/AR/mace/
McCune, W.: Otter 3.3 reference manual. Tech. Rep. ANL/MCS-TM-263, Argonne Nat. Lab., Math. and Comp. Sci. Div. (2003), Available at, http://www-unix.mcs.anl.gov/AR/otter/
McKay, B.D.: Nauty user’s guide, version 2.2 (2003), Available at, http://cs.anu.edu.au/~bdm/nauty/nug.pdf
Meseguer, P., Torras, C.: Solving strategies for highly symmetric CSPs. In: Proc. of IJCAI 1999. Morgan Kaufmann, San Francisco (1999)
Riazanov, A., Voronkov, A.: Vampire. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 292–296. Springer, Heidelberg (1999)
Van Hentenryck, P.: The OPL Optimization Programming Language. The MIT Press, Cambridge (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cadoli, M., Mancini, T. (2005). Using a Theorem Prover for Reasoning on Constraint Problems. In: Bandini, S., Manzoni, S. (eds) AI*IA 2005: Advances in Artificial Intelligence. AI*IA 2005. Lecture Notes in Computer Science(), vol 3673. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11558590_4
Download citation
DOI: https://doi.org/10.1007/11558590_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29041-4
Online ISBN: 978-3-540-31733-3
eBook Packages: Computer ScienceComputer Science (R0)