Representations of monotone Boolean functions by linear programs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00511322" target="_blank" >RIV/67985840:_____/19:00511322 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1145/3337787" target="_blank" >http://dx.doi.org/10.1145/3337787</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1145/3337787" target="_blank" >10.1145/3337787</a>

Result language
angličtina
Original language name
Representations of monotone Boolean functions by linear programs
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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