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Everything about AC0

Complexity class of bounded-depth circuits

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 circuits are called "alternating circuits", since it is only necessary for the layers to alternate between all-AND and all-OR, since one AND after another AND is equivalent to a single AND, and the same for OR. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: AC0A 5-minute orientation
  2. Pick up a classic book: Student Manual : Adobe Acrobat 7. 0 ProfessionalThe most-reprinted book on the subject
  3. Read the landmark paper: Probabilistic polynomials, AC0 functions and the polynomial-time hierarchyCited 40 times
  4. Go sideways: TC0A closely related topic
  5. Go sideways: Circuit complexityA closely related topic

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🏆 Landmark papers (most cited)

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