AC0, NC1, and NC under a stated uniformity convention

All families in this definition are logspace-uniform. For bounded-fan-in families this means exactly the query interface of A logspace-uniform Boolean circuit family. For an unbounded-fan-in gate, the same interface is extended by a fan-in query and by predecessor queries $(v,j)$ that return the $j$-th predecessor of gate $v$ (or report that $j$ is out of range); the transducer must answer all such queries in logarithmic space.

${\mathrm{A}\mathrm{C}}^0$ has polynomial size, constant depth, unbounded-fan-in AND/OR, and NOT gates. ${\mathrm{N}\mathrm{C}}^1$ has polynomial size, bounded fan-in, and logarithmic depth. $\mathrm{N}\mathrm{C}$ is the union of polynomial-size bounded-fan-in families of polylogarithmic depth. This convention does not constrain arbitrary $\mathrm{P}\mathrm{/}\mathrm{p}\mathrm{o}\mathrm{l}\mathrm{y}$ families.