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The problem is complete for [[P_(complexity) | 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 [[NC_(complexity) | NC1]]<ref>{{cite web|last1=Samuel|first1=Buss|title=Boolean formula value problem (BFVP) in Alogtime |url=http://www.math.ucsd.edu/~sbuss/ResearchWeb/Boolean/|website=www.math.ucsd.edu|accessdate=3 April 2016}}</ref>
The problem is closely related to [[Boolean satisfiability problem | Boolean Satisfiability Problem]] which is complete for [[NP_(complexity) | NP]] and its complement [[Tautology_(logic) | Propositional Tautologihood Problem]] which is complete for [[Co-NP | coNP]].
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