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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 $n$ inputs each take one gate. Testing equality of two $n$-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.

The parity function on bits returns whether an odd number of them are one:For example, ${\mathrm{PARITY}}_4(1,0,1,1)=1$, and flipping any single input flips the output. A chain of exclusive or gates computes it with $n-1$ gates and linear depth; a balanced binary tree of such gates has logarithmic depth and still linear size.

Appending a parity bit to make the total even detects every single-bit error in a transmitted binary string. It misses any even number of flipped bits, because their changes cancel modulo two. This simple example separates error detection from error correction: detecting an odd number of changes does not identify which positions changed.