Representations of Monotone Boolean Functions by Linear Programs

We introduce the notion of monotone linear-programming circuits (MLP circuits), a model of computation for partial Boolean functions. Using this model, we prove the following results. 1. MLP circuits are superpolynomially stronger than monotone Boolean circuits. 2. MLP circuits are exponentially stronger than monotone span programs. 3. MLP circuits can be used to provide monotone feasibility interpolation theorems for LovászSchrijver proof systems, and for mixed Lovász-Schrijver proof systems. 4. The Lovász-Schrijver proof system cannot be polynomially simulated by the cutting planes proof system. This is the first result showing a separation between these two proof systems. Finally, we discuss connections between the problem of proving lower bounds on the size of MLPs and the problem of proving lower bounds on extended formulations of polytopes. 1998 ACM Subject Classification F.2.2 [Nonnumerical Algorithms and Problems] Complexity of Proof Procedures