Representations of monotone Boolean functions by linear programs

0511322 - MÚ 2020 RIV US eng J - Journal Article
de Oliveira Oliveira, M. - Pudlák, Pavel
Representations of monotone Boolean functions by linear programs.
ACM Transactions on Computation Theory. Roč. 11, č. 4 (2019), č. článku 22. ISSN 1942-3454
EU Projects: European Commission(XE) 339691 - FEALORA
Institutional support: RVO:67985840
Keywords : monotone linear programming circuits * Lovász-Schrijver proof systems * feasible interpolation
OECD category: Pure mathematics
Method of publishing: Open access
http://dx.doi.org/10.1145/3337787

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 over the reals. (3) MLP circuits can be used to provide monotone feasibility interpolation theorems for Lovász-Schrijver 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. Finally, we establish connections between the problem of proving lower bounds for the size of MLP circuits and the field of extension complexity of polytopes.
Permanent Link: http://hdl.handle.net/11104/0301620