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AC0

AC0 (alternating circuit) is a complexity class used in circuit complexity. It is the smallest class in the AC hierarchy, and consists of all families of circuits of depth O(1) and polynomial size, with unlimited-fanin AND gates and OR gates (we allow NOT gates only at the inputs). It thus contains NC0, which has only bounded-fanin AND and OR gates. Such…

Descriptive complexity, Separations & Example problems

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Descriptive complexity

Descriptive complexityDLOGTIMEUniformFOLanguages
8 related topics

Separations

SipserPARITYTC0XOR
4 related topics

Example problems

P/polyUnary language
2 related topics

Overview

Complexity classCircuit complexityACFaninAND gates
8 related topics

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Overview

Example problems

Descriptive complexity

Separations

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Map overview Semantic statistics

AC0

Nodes27
Edges26
Triples20
Avg. degree1.93
Density0.074074
Components1

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AC0

Top relations

related to Separations · 12
AC0 → AC, Furst, However, In, It, Note, PARITY, Saxe, Similarly, Sipser, TC0, XOR
related to Descriptive complexity · 5
AC0 → BIT, DLOGTIME-uniform AC0, FO, From, Turing
related to Example problems · 3
AC0 → Integer, P/poly, Since

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Important terminology

class circuits ac displaystyle alternating depth complexity addition two mathsf circuit hierarchy size inputs gates languages parity also family polynomial

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
AC0related to Descriptive complexityFrom0.60section
AC0related to Descriptive complexityDLOGTIME-uniform AC00.60section
AC0related to Descriptive complexityFO0.60section
AC0related to Descriptive complexityBIT0.60section
AC0related to Descriptive complexityTuring0.60section
AC0related to Example problemsInteger0.60section
AC0related to Example problemsSince0.60section
AC0related to Example problemsP/poly0.60section
AC0related to SeparationsIn0.60section
AC0related to SeparationsFurst0.60section
AC0related to SeparationsSaxe0.60section
AC0related to SeparationsSipser0.60section

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    Min side: 3
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