The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
The OPL optimization programming language
The OPL optimization programming language
Exploiting symmetries within constraint satisfaction search
Artificial Intelligence - Special issue on heuristic search in artificial intelligence
Logic programs with stable model semantics as a constraint programming paradigm
Annals of Mathematics and Artificial Intelligence
Backtrack Searching in the Presence of Symmetry
AAECC-6 Proceedings of the 6th International Conference, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On the Satisfiability of Symmetrical Constrained Satisfaction Problems
ISMIS '93 Proceedings of the 7th International Symposium on Methodologies for Intelligent Systems
Global Cut Framework for Removing Symmetries
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Dual Models of Permutation Problems
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Breaking Row and Column Symmetries in Matrix Models
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Breaking Instance-Independent Symmetries in Exact Graph Coloring
Proceedings of the conference on Design, automation and test in Europe - Volume 1
The DLV system for knowledge representation and reasoning
ACM Transactions on Computational Logic (TOCL)
Solving strategies for highly symmetric CSPs
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
Tractable symmetry breaking for CSPs with interchangeable values
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Compiling problem specifications into SAT
Artificial Intelligence - Special volume on reformulation
Automated reformulation of specifications by safe delay of constraints
Artificial Intelligence
Exploiting functional dependencies in declarative problem specifications
Artificial Intelligence
USING A THEOREM PROVER FOR REASONING ON CONSTRAINT PROBLEMS
Applied Artificial Intelligence
Expressive power and abstraction in Essence
Constraints
Evaluating ASP and commercial solvers on the CSPLib
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
A unifying framework for structural properties of CSPs: definitions, complexity, tractabilit
Journal of Artificial Intelligence Research
Automated reformulation of specifications by safe delay of constraints
Artificial Intelligence
A novel approach for detecting symmetries in CSP models
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
A 25-year perspective on logic programming
Proving symmetries by model transformation
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Using a theorem prover for reasoning on constraint problems
AI*IA'05 Proceedings of the 9th conference on Advances in Artificial Intelligence
SAT as an effective solving technology for constraint problems
ISMIS'06 Proceedings of the 16th international conference on Foundations of Intelligent Systems
Scheduling social golfers with memetic evolutionary programming
HM'06 Proceedings of the Third international conference on Hybrid Metaheuristics
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In this paper we address the problem of detecting and breaking symmetries in combinatorial problems, following the approach of imposing additional symmetry-breaking constraints. Differently from other works in the literature, we attack the problem at the specification level. In fact, many symmetries depend on the structure of the problem, and not on the particular input instance. Hence, they can be easily detected by reasoning on the specification, and appropriate symmetry-breaking formulae generated. We give formal definitions of symmetries and symmetry-breaking formulae on specifications written in existential second-order logic, clarifying the new definitions on some specifications: Graph 3-coloring, Social golfer, and Protein folding problems. Finally, we show experimentally that, applying this technique, even if in a naive way, to specifications written in state-of-the-art languages, e.g., opl, may greatly improve search efficiency.