TC0 contains all languages which are decided by Boolean circuits with constant depth and polynomial size, containing only unbounded fan-in AND gates, OR gates, NOT gates, and majority gates. Equivalently, threshold gates can be used instead of majority gates.
TC0 contains several important problems, such as sorting n n-bit numbers, multiplying two n-bit numbers, integer division or recognizing the Dyck language with two types of parentheses.
Complexity class relations
Vollmer states that the question of whether the last inclusion above is strict is "one of the main open problems in circuit complexity" (ibid.).
We also have that uniform . (Allender 1996, as cited in Burtschick 1999).
Basis for uniform
The functional version of the uniform coincides with the closure with respect to composition of the projections and one of the following function sets , . Here , is a bitwise AND of and . By functional version one means the set of all functions over non-negative integers that are bounded by functions of FP and is in the uniform .
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