A new algorithm for the binate covering problem and its application to the minimization of Boolean relations

~~e$;te -Covering Problem (BCP) is the problem of mrmmum cost assrgnment to varmbles that rs a solution of a boolean equation f = 1. It is a Keeneralisation of the set covering (or &ate covering) prlblem, where f is positive unate. and is generally given as a table with rows corresponding to th; set eie;ents and the columns corresponding to the subsets. Previous methods have considered the case when f is given as a product-ofsum formula or as a binary decision diagram (BDD). In thrs paper we present a new branch-and-bound algorrthm for the BCP, that assumes f is expressed as the conjunction of multiple BDD’s. The BCP solver we have implemented can be applied to several problems, including exact minimisation of boolean relations, for which we present results. We have been able to solve large, difficult problems (up to 4692 variables) which could not be solved by the product of sum-based method.