Circuit Value Problem

The Circuit Value Problem (or Circuit Evaluation Problem) is the computational problem of computing the output of a given Boolean circuit on a given input.

Boolean example circuit

The problem is complete for P under uniform AC0 reductions. Note that, in terms of time complexity, it can be solved in linear time simply by a topological sort.

The Boolean Formula Value Problem (or 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.[1]

The problem is closely related to the Boolean Satisfiability Problem which is complete for NP and its complement, the Propositional Tautology Problem, which is complete for co-NP.

References
  1. Buss, Samuel R. (January 1987). "The Boolean formula value problem is in ALOGTIME". www.math.ucsd.edu. Retrieved May 5, 2017.


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