文章基本信息

标题：Representations of Monotone Boolean Functions by Linear Programs
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作者：Mateus de Oliveira Oliveira ; Pavel Pudl{\'a}k
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2017
卷号：79
页码：3:1-3:14
DOI：10.4230/LIPIcs.CCC.2017.3
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：Monotone Linear Programming Circuits; Lov{\'a