The Circuit Value Problem (aka. the Circuit Evaluation Problem) is the computational problem of computing the output of a given Boolean circuit on a given input.
The problem is complete for P under uniform AC0 reductions. The Boolean Formula Value Problem (aka. Boolean Formula Evaluation Problem) is the special case of the problem when the circuit is a tree. The Boolean Formula Value Problem is complete for NC1
The problem is closely related to Boolean Satisfiability Problem which is complete for NP and its complement Propositional Tautologihood Problem which is complete for coNP.
References
Circuit Value Problem Wikipedia(Text) CC BY-SA