Doubly lexical orderings of matrices
SIAM Journal on Computing
ECAI '92 Proceedings of the 10th European conference on Artificial intelligence
Better verification through symmetry
Formal Methods in System Design - Special issue on symmetry in automatic verification
Isomorph-free model enumeration: a new method for checking relational specifications
ACM Transactions on Programming Languages and Systems (TOPLAS)
Isomorph-free exhaustive generation
Journal of Algorithms
Alcoa: the alloy constraint analyzer
Proceedings of the 22nd international conference on Software engineering
Self-stabilizing systems in spite of distributed control
Communications of the ACM
Chord: A scalable peer-to-peer lookup service for internet applications
Proceedings of the 2001 conference on Applications, technologies, architectures, and protocols for computer communications
Proceedings of the 8th European software engineering conference held jointly with 9th ACM SIGSOFT international symposium on Foundations of software engineering
On the Satisfiability of Symmetrical Constrained Satisfaction Problems
ISMIS '93 Proceedings of the 7th International Symposium on Methodologies for Intelligent Systems
Counting Models Using Connected Components
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Breaking Row and Column Symmetries in Matrix Models
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Exploring the Design of an Intentional Naming Scheme with an Automatic Constraint Analyzer
ASE '00 Proceedings of the 15th IEEE international conference on Automated software engineering
Software Abstractions: Logic, Language, and Analysis
Software Abstractions: Logic, Language, and Analysis
Efficient symmetry breaking for boolean satisfiability
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Exploiting symmetry in lifted CSPs
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Propagation algorithms for lexicographic ordering constraints
Artificial Intelligence
A constraint-based approach to Enigma 1225
Computers & Mathematics with Applications
An Empirical Study of Structural Constraint Solving Techniques
ICFEM '09 Proceedings of the 11th International Conference on Formal Engineering Methods: Formal Methods and Software Engineering
Combination: automated generation of puzzles with constraints
Proceedings of the 2011 ACM Symposium on Applied Computing
An approach for effective design space exploration
FOCS'10 Proceedings of the 16th Monterey conference on Foundations of computer software: modeling, development, and verification of adaptive systems
Synthesis of first-order dynamic programming algorithms
Proceedings of the 2011 ACM international conference on Object oriented programming systems languages and applications
Proceedings of the 17th ACM SIGPLAN international conference on Functional programming
Pattern-guided genetic programming
Proceedings of the 15th annual conference on Genetic and evolutionary computation
Aluminum: principled scenario exploration through minimality
Proceedings of the 2013 International Conference on Software Engineering
Breaking symmetries in graph representation
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Consider the problem of testing for existence of an n-node graph G satisfying some condition P, expressed as a Boolean constraint among the nxn Boolean entries of the adjacency matrix M. This problem reduces to satisfiability of P(M). If P is preserved by isomorphism, P(M) is satisfiable iff P(M)@?SB(M) is satisfiable, where SB(M) is a symmetry-breaking predicate-a predicate satisfied by at least one matrix M in each isomorphism class. P(M)@?SB(M) is more constrained than P(M), so it is solved faster by backtracking than P(M)-especially if SB(M) rules out most matrices in each isomorphism class. This method, proposed by Crawford et al., applies not just to graphs but to testing existence of a combinatorial object satisfying any property that respects isomorphism, as long as the property can be compactly specified as a Boolean constraint on the object's binary representation. We present methods for generating symmetry-breaking predicates for several classes of combinatorial objects: acyclic digraphs, permutations, functions, and arbitrary-arity relations (direct products). We define a uniform optimality measure for symmetry-breaking predicates, and evaluate our constraints according to this measure. Results indicate that these constraints are either optimal or near-optimal for their respective classes of objects.