Groups and Constraints : Symmetry Breaking During Sear h ?

Groups and Constraints : Symmetry Breaking During Sear hIan

Dynamic Symmetry Breaking Constraints

We present a general method for dynamically posting symmetry breaking constraints during search. The basic idea is very simple. Given any set of symmetry breaking constraints, if during search a symmetry of one of these constraints is entailed and this is consistent with previously posted symmetry breaking constraints, then we post this constraint. We illustrate the method with two examples whe...

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The nature of axion cosmology is usually said to depend on whether the Peccei-Quinn (PQ) symmetry breaks before or after inflation. The PQ symmetry itself is believed to be an accident, so there is not necessarily a symmetry during inflation at all. We explore these issues in some simple models, which provide examples of symmetry breaking before and after inflation, or in which there is no symm...

Posting Static Symmetry Breaking Constraints Dynamically

Symmetry is an important feature of many combinatorial search problems. We propose a new method for dynamically posting static symmetry breaking constraints during search. This method is based on the observations that any symmetry of a set of symmetry breaking constraints can be used to break symmetry, and different symmetries pick out different solutions. We choose which symmetry to post as br...

Reducing Symmetry in Matrix Models: SBDS v. Constraints

We discuss diierent methods of reducing symmetry in CSPs where the variables correspond to the cells of a matrix, and both the rows and the columns of the matrix are interchangeable. Two basic approaches are considered: adding symmetry-breaking constraints to the model, and breaking symmetry during search. We also show how the two approaches can be combined in this case. We empirically compare ...