AC0 is the class of decision problems computable by Boolean circuit families with polynomial circuit size, constant circuit depth and unbounded-fan-in AND gates and OR gates, together with NOT gates. The depth bound is independent of input length. Uniform and nonuniform versions must be distinguished; without a qualifier the Circuit family need not be generated by one efficient algorithm.
Conjunction and disjunction of inputs each take one gate. Testing equality of two -bit strings also has constant depth: test equality at every bit using a fixed small circuit, then AND those results. In contrast, the parity function cannot be computed by constant-depth polynomial-size circuits of this gate basis. Adding an unbounded parity gate changes the model and defeats that conclusion. Counting only depth while ignoring size would also be misleading: a truth-table Disjunctive normal form represents any Boolean function at constant depth but may require exponentially many gates.
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