TC (complexity)

In theoretical computer science, and specifically computational complexity theory and circuit complexity, TC is a complexity class of decision problems that can be recognized by threshold circuits, which are Boolean circuits with AND, OR, and Majority gates. For each fixed i, the complexity class TCⁱ consists of all languages that can be recognized by a family of threshold circuits of depth ${\displaystyle O(\log ^{i}n)}$, polynomial size, and unbounded fan-in. The class TC is defined via

${\displaystyle {\mbox{TC}}=\bigcup _{i\geq 0}{\mbox{TC}}^{i}.}$