Circuit value problem: Difference between revisions

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{{Short description|Computational problem}}

The '''Circuit Value Problem''' (aka. the Circuit Evaluation Problem)

[[File:Combinatorial Logic Example.svg|thumb|An example Boolean circuit]]

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.

The problem is complete for [[P_P (complexity) | P]] under uniform [[AC0|AC{{sup|0}}]] 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]] (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]]<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 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 [[NC (complexity)|NC{{sup|1}}]] with respect to AC{{sup|0}} reductions.<ref>{{cite conference | url=https://dl.acm.org/doi/pdf/10.1145/28395.28409 | author=Samuel R. Buss | author-link=Samuel Buss | title=The Boolean formula value problem is in ALOGTIME | editor=Alfred V. Aho | editor-link=Alfred Aho| book-title=Proceedings of the 19th Annual ACM [[Symposium on Theory of Computing]] (STOC) | publisher=ACM | pages=123&ndash;131 | date=Jan 1987 | doi=10.1145/28395.28409 | url-access=subscription }} ([http://www.math.ucsd.edu/~sbuss/ResearchWeb/Boolean Author's draft])</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]].

The problem is closely related to the [[Boolean satisfiability problem | Boolean Satisfiability Problem]] which is complete for [[NP_NP (complexity) | NP]] and its complement, the [[Tautology_Tautology (logic) |propositional Propositionaltautology Tautologihood Problemproblem]], which is complete for [[Coco-NP | coNP]].

== ReferencesSee also ==

* [[Circuit satisfiability]]

* [[Switching lemma]]

==References==

{{Reflist}}

* {{cite journal | url= | doi=10.1145/990518.990519 | author=Richard E. Ladner | author-link=Richard E. Ladner | title=The circuit value problem is log space complete for P | journal=[[ACM SIGACT News]] | volume=7 | number=101 | pages=18&ndash;20 | date=Jan 1975 }}

[[Category:Polynomial-time problems]]

[[Category:Computational problems]]

[[Category:Complexity theory]]

[[Category:Theoretical computer science]]

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