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Representations of Monotone Boolean Functions by Linear Programs

Authors Mateus de Oliveira Oliveira, Pavel Pudlák

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Keywords
  • Monotone Linear Programming Circuits
  • Lovász-Schrijver Proof System
  • Cutting-Planes Proof System
  • Feasible Interpolation
  • Lower Bounds

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Abstract

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 Lovasz-Schrijver  proof systems, and for mixed Lovasz-Schrijver  proof systems.

4. The Lovasz-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.

Cite As Get BibTex

Mateus de Oliveira Oliveira and Pavel Pudlák. Representations of Monotone Boolean Functions by Linear Programs. In 32nd Computational Complexity Conference (CCC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 79, pp. 3:1-3:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.CCC.2017.3

Author Details

Mateus de Oliveira Oliveira
Pavel Pudlák

References

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