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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.

Circuit complexity measures the resources of Boolean circuits computing a Boolean function. Circuit size counts logic gates or wires under a declared convention; circuit depth measures the longest dependency chain. The allowed logic gates and their fan-in are part of the model.

For the conjunction of $n$ Boolean variables, a chain of two-input AND gates uses $n-1$ logic gates and depth $n-1$. A balanced binary tree still uses $n-1$ logic gates but reduces depth to $\lceil {\log }_{2}n\rceil$. A depth-$d$ Boolean circuit of fan-in at most two can depend on at most $2^d$ inputs, so that depth is optimal for this function. An unbounded-fan-in AND gate would compute it in one layer, showing why the logic gate convention matters.

A circuit family supplies one Boolean circuit per input length. uniform circuit families impose an effective construction rule; an unrestricted nonuniform family can choose separate Boolean circuits independently. Lower bounds therefore need both the Boolean circuit model and the uniformity convention.

A model of computation specifies how inputs are represented, which states and operations are available, how execution proceeds and what counts as its output and resource cost. Examples include Turing machines, random-access machines, Boolean circuits and the lambda calculus. A mathematical algorithmic claim is interpreted within such a model, even when the model is left implicit.

For example, adding two integers is one instruction in a unit-cost machine model. In a bit-cost model, operating on arbitrarily long integers requires time depending on their encoded lengths. A bound counting arithmetic operations therefore need not be a bound on bit complexity. Likewise, a circuit family can supply separate hardware for each input length, while a uniformity requirement asks one algorithm to generate those circuits. Stating the model makes efficiency comparisons meaningful and separates questions of computability from the cost of a chosen representation.

For each fixed input length, take the complete truth table of the language. For every accepted string $z\in \{0,1{\}}^n$, form the mintermAn OR of these minterms equals the indicator function, since $M_z(x)=1$ precisely at $x=z$. This is the truth-table upper bound for circuit size.

Generate the $n$ negated input wires once and share them. With $m\le 2^n$ accepted strings, use at most $m(n-1)$ binary AND gates and $m-1$ binary OR gates, besides the negations. Empty truth tables use a constant-zero Boolean circuit; length zero is handled by a constant Boolean circuit. ThusThis is an existence bound for a nonuniform circuit family, even when the language is undecidable. It supplies no algorithm for computing the truth tables of an arbitrary language.