Symmetry Breaking Revisited

Foundations of Symmetry Breaking Revisited

Puget’s article “On the Satisfiability of Symmetrical Constraint Satisfaction Problems” [Puget, 1993] is widely acknowledged to be one of the founding papers in symmetry breaking (see for example [Flener et al., 2006; Rossi et al., 2006; Walsh, 2006]). To date, Puget’s definition of a valid reduction seems to be the only common ground that all authors on static symmetry breaking constraints agr...

Foundations of Symmetry Breaking Revisited–Revised

Puget’s article “On the Satisfiability of Symmetrical Constraint Satisfaction Problems” [Puget, 1993] is widely acknowledged to be one of the founding papers in symmetry breaking (see for example [Flener et al., 2006; Rossi et al., 2006; Walsh, 2006]). To date, Puget’s definition of a valid reduction seems to be the only common ground that all authors on static symmetry breaking constraints agr...

Symmetry Breaking

Symmetry occurs in many problems in aritifical intelligence. For example, in the n-queens problem, the chessboard can be rotated 90◦. As a second example, several machines in a factory might have the same capacity. In a production schedule, we might therefore be able to swap the jobs on machines with the same capacity. As a third example, two people within a company might have the same skills. ...

Symmetry Breaking

Symmetry, Symmetry Breaking and Topology

The ground state of a system with symmetry can be described by a group G. This symmetry groupG can be discrete or continuous. Thus for a crystalG is a finite group while for the vacuum state of a grand unified theory G is a continuous Lie group. The ground state symmetry described by G can change spontaneously from G to one of its subgroups H as the external parameters of the system are modifie...