Artificial intelligence: a modern approach
Artificial intelligence: a modern approach
Better verification through symmetry
Formal Methods in System Design - Special issue on symmetry in automatic verification
Exploiting symmetry in temporal logic model checking
Formal Methods in System Design - Special issue on symmetry in automatic verification
Formal Methods in System Design - Special issue on symmetry in automatic verification
Formal Methods in System Design - Special issue on The First Federated Logic Conference (FLOC'96), part II
Model checking
SMC: a symmetry-based model checker for verification of safety and liveness properties
ACM Transactions on Software Engineering and Methodology (TOSEM)
Symbolic Model Checking
Groups and Constraints: Symmetry Breaking during Search
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Symmetry Reductions inModel Checking
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
Exploiting structure in symmetry detection for CNF
Proceedings of the 41st annual Design Automation Conference
Finding the smallest image of a set
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Symmetry in temporal logic model checking
ACM Computing Surveys (CSUR)
Extending Symmetry Reduction Techniques to a Realistic Model of Computation
Electronic Notes in Theoretical Computer Science (ENTCS)
Spin model checker, the: primer and reference manual
Spin model checker, the: primer and reference manual
Spin-to-Grape: A Tool for Analysing Symmetry in Promela Models
Electronic Notes in Theoretical Computer Science (ENTCS)
Automatic symmetry detection for model checking using computational group theory
FM'05 Proceedings of the 2005 international conference on Formal Methods
Symmetry reduction for probabilistic model checking
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Exact and approximate strategies for symmetry reduction in model checking
FM'06 Proceedings of the 14th international conference on Formal Methods
A computational group theoretic symmetry reduction package for the SPIN model checker
AMAST'06 Proceedings of the 11th international conference on Algebraic Methodology and Software Technology
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Symmetry reduction techniques aim to combat the state-space explosion problem for model checking by restricting search to representative states from equivalence classes with respect to a group of symmetries. The standard approach to representative computation involves converting a state to its minimal image under a permutation group G, before storing the state. This is known as the constructive orbit problem (COP), and is ${\mathit{NP}}$ hard. It may be possible to solve the COP efficiently if G is known to have certain structural properties: in particular if G is isomorphic to a full symmetry group, or G is a disjoint/wreath product of subgroups. We extend existing results on solving the COP efficiently for fully symmetric groups, and investigate the problem of automatically classifying an arbitrary permutation group as a disjoint/wreath product of subgroups. We also present an approximate COP strategy based on local search, and some computational group-theoretic optimisations to improve the basic approach of solving the COP by symmetry group enumeration. Experimental results using the TopSPIN symmetry reduction package, which interfaces with the computational group-theoretic system GAP, illustrate the effectiveness of our techniques.