Hostname: page-component-8448b6f56d-gtxcr Total loading time: 0 Render date: 2024-04-23T08:28:00.477Z Has data issue: false hasContentIssue false
  • English
  • Français

On local domain symmetry for model expansion

Published online by Cambridge University Press:  14 October 2016

JO DEVRIENDT ,
BART BOGAERTS ,
MAURICE BRUYNOOGHE  and
MARC DENECKER
JO DEVRIENDT
Affiliation:
KU Leuven – University of Leuven, Celestijnenlaan 200A, Leuven, Belgium (e-mail: firstname.lastname@cs.kuleuven.be)
BART BOGAERTS
Affiliation:
KU Leuven – University of Leuven, Celestijnenlaan 200A, Leuven, Belgium (e-mail: firstname.lastname@cs.kuleuven.be) Helsinki Institute for Information Technology HIIT, Aalto University, FI-00076 AALTO, Finland
MAURICE BRUYNOOGHE
Affiliation:
KU Leuven – University of Leuven, Celestijnenlaan 200A, Leuven, Belgium (e-mail: firstname.lastname@cs.kuleuven.be)
MARC DENECKER
Affiliation:
KU Leuven – University of Leuven, Celestijnenlaan 200A, Leuven, Belgium (e-mail: firstname.lastname@cs.kuleuven.be)
Get access Rights & Permissions [Opens in a new window]

Abstract

Symmetry in combinatorial problems is an extensively studied topic. We continue this research in the context of model expansion problems, with the aim of automating the workflow of detecting and breaking symmetry. We focus on local domain symmetry, which is induced by permutations of domain elements, and which can be detected on a first-order level. As such, our work is a continuation of the symmetry exploitation techniques of model generation systems, while it differs from more recent symmetry breaking techniques in answer set programming which detect symmetry on ground programs. Our main contributions are sufficient conditions for symmetry of model expansion problems, the identification of local domain interchangeability, which can often be broken completely, and efficient symmetry detection algorithms for both local domain interchangeability as well as local domain symmetry in general. Our approach is implemented in the model expansion system IDP, and we present experimental results showcasing the strong and weak points of our approach compared to sbass, a symmetry breaking technique for answer set programming.

Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 16 , Special Issue 5-6: 32nd International Conference on Logic Programming , September 2016 , pp. 636 - 652
Copyright
Copyright © Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aloul, F., Ramani, A., Markov, I. and Sakallah, K. 2002. Solving difficult SAT instances in the presence of symmetry. In Design Automation Conference, 2002. Proceedings. 39th. 731–736.Google Scholar
Aloul, F. A., Sakallah, K. A. and Markov, I. L. 2006. Efficient symmetry breaking for Boolean satisfiability. IEEE Transactions on Computers 55, 5, 549–558.CrossRefGoogle Scholar
Audemard, G. and Benhamou, B. 2002. Reasoning by symmetry and function ordering in finite model generation. In Automated Deduction - CADE-18, 18th International Conference on Automated Deduction, Copenhagen, Denmark, July 27-30, 2002, Proceedings, Voronkov, A., Ed. Lecture Notes in Computer Science, vol. 2392. Springer, 226–240.Google Scholar
Claessen, K. and Sörensson, N. 2003. New Techniques that Improve MACE-style Model Finding. In Workshop on Model Computation (MODEL).Google Scholar
De Cat, B., Bogaerts, B., Bruynooghe, M., Janssens, G. and Denecker, M. 2016. Predicate logic as a modelling language: The IDP system. CoRR abs/1401.6312v2.Google Scholar
Denecker, M. and Ternovska, E. 2008. A logic of nonmonotone inductive definitions. ACM Trans. Comput. Log. 9, 2 (Apr.), 14:1–14:52.CrossRefGoogle Scholar
Devriendt, J., Bogaerts, B. and Bruynooghe, M. 2014. BreakIDGlucose: On the importance of row symmetry in SAT. In Proceedings of the Fourth International Workshop on the Cross-Fertilization Between CSP and SAT (CSPSAT).Google Scholar
Devriendt, J., Bogaerts, B., Bruynooghe, M. and Denecker, M. 2016. On local domain symmetry for model expansion. Available at http://arxiv.org/abs/1608.02688.Google Scholar
Drescher, C., Tifrea, O. and Walsh, T. 2011. Symmetry-breaking answer set solving. IA Communications 24, 2, 177–194.Google Scholar
Enderton, H. B. 2001. A Mathematical Introduction To Logic, Second ed. Academic Press.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B. and Schaub, T. 2014. Clingo = ASP + control: Preliminary report. In Technical Communications of the Thirtieth International Conference on Logic Programming (ICLP'14), Leuschel, M. and Schrijvers, T., Eds. Vol. 14(4-5). Online Supplement.Google Scholar
Gent, I. P., Petrie, K. E. and Puget, J.-F. 2006. Symmetry in constraint programming. Handbook of Constraint Programming 10, 329–376.CrossRefGoogle Scholar
Katebi, H., Sakallah, K. A. and Markov, I. L. 2010. Symmetry and satisfiability: An update. In SAT, Strichman, O. and Szeider, S., Eds. LNCS, vol. 6175. Springer, 113–127.Google Scholar
Sakallah, K. A. 2009. Symmetry and Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press, Chapter 10, 289–338.Google Scholar
Shlyakhter, I. 2007. Generating effective symmetry-breaking predicates for search problems. Discrete Appl. Math. 155, 12 (June), 1539–1548.CrossRefGoogle Scholar
Torlak, E. and Jackson, D. 2007. Kodkod: A relational model finder. In TACAS, Grumberg, O. and Huth, M., Eds. LNCS, vol. 4424. Springer, 632–647.Google Scholar
Walsh, T. 2012. Symmetry breaking constraints: Recent results. CoRR abs/1204.3348.Google Scholar
Zhang, J. and Zhang, H. 1995. Sem: A system for enumerating models. In Department of Philosophy University of Wisconsin-Madison Mathematics and Computer Science. 298–303.Google Scholar