Detecting and breaking symmetries on specifications

In this paper we address symmetry on combinatorial problems by 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, sometimes symmetries on specifications can be very easily detected, and symmetry-breaking formulae generated. We give formal definitions of symmetries and symmetrybreaking formulae on specifications written in existential second-order logic, clarifying the new definitions on two specifications: the graph 3coloring and the social golfer problems. Finally, we show the results of a preliminary experimentation of our techiques on examples using stateof-the-art linear and constraint programming solvers.