Efficient Binary Linear Programming Formulations for Boolean Functions

Frank Gurski
2014 Statistics, Optimization and Information Computing  
A very useful tool when designing linear programs for optimization problems is the formulation of logical operations by linear programming constraints. We give efficient linear programming formulation of important n-ary boolean functions f (x 1 , . . . , xn) = x n+1 such as conjunction, disjunction, equivalence, and implication using n + 1 boolean variables x 1 , . . . , x n+1 . For the case that the value f (x 1 , . . . , xn) is not needed for further computations, we even give a more compact
more » ... ive a more compact formulation. Our formulations show that every binary boolean function f (x 1 , x 2 ) = x 3 can be realized by the only three boolean variables x 1 ,x 2 ,x 3 and at most four linear programming constraints.
doi:10.19139/soic.v2i4.83 fatcat:iosfddfh4jghzdsjwqqwrbdkeu