βkMAC0 is the class of decision problems solvable by a uniform family of polynomial-sized MAC0 circuits that accept O(logk n) nondeterministic input bits, with the same acceptance mechanism as MAC0.
βMAC0 is the union of βkMAC0 over all constant k.
For any constant k, βkMAC0 is contained in βkTC0. In particular, β1MAC0 is contained in β1TC0 = TC0.
We note that βkMAC0 = NMAC0(logk n).
The notion of a non-deterministic NC circuit was introduced in [Wol94]; see NNC(f(n)).
No class.