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Boolean hierarchy

The Boolean hierarchy is the hierarchy of Boolean combinations (intersection, union and complementation) of NP sets. Equivalently, the Boolean hierarchy can be described as the class of Boolean circuits over NP predicates. A collapse of the Boolean hierarchy would imply a collapse of the polynomial hierarchy.

Formal definition, Hardness & Overview

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Explore the main themes, entities and connections around Boolean hierarchy. Start with the topic map, then use the sections below for research and deeper semantic analysis.

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Formal definition

CoNP
1 related topics

Hardness

NP-complete
1 related topics

Overview

HierarchyBoolean combinationsIntersectionUnionComplementation
9 related topics

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Overview

Formal definition

Hardness

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Map overview Semantic statistics

Boolean hierarchy

Nodes15
Edges14
Triples6
Avg. degree1.87
Density0.133333
Components1

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Boolean hierarchy

Top relations

related to Hardness · 5
Boolean hierarchy → BH2k-hardness, Boolean, Hardness, In, NP-complete
is a · 1
Boolean hierarchy → hierarchy of Boolean combinations

Important terminology Word statistics

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Important terminology

hierarchy np boolean classes intersection union class definitions defined follows bh2k languages language polynomial definition hardness conp complementation bh dp

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Boolean hierarchyis ahierarchy of Boolean combinations0.90text
Boolean hierarchyrelated to HardnessHardness0.60section
Boolean hierarchyrelated to HardnessBoolean0.60section
Boolean hierarchyrelated to HardnessNP-complete0.60section
Boolean hierarchyrelated to HardnessIn0.60section
Boolean hierarchyrelated to HardnessBH2k-hardness0.60section

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    Min side: 3
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