Lesson plan
Counting problem (complexity)
In computational complexity theory and computability theory, a counting problem is a type of computational problem that is obtained by strengthening a decision problem. For example, the SAT problem asks: "Given a Boolean formula, is there a truth-value assignment such that it evaluates to True?". The corresponding counting problem, called #SAT, asks: "Given a Boolean formula, how many truth-value assignments are there such that it evaluates to True?". And in general, the counting problem corresponding to a decision problem X is called #X, where # is the number sign. Counting complexity techniques have significant applications in clarifying the relation between complexity classes of P, NP, PH, etc, in circuit complexity, and in interactive proof systems.
Article summary
In computational complexity theory and computability theory, a counting problem is a type of computational problem that is obtained by strengthening a decision problem. For example, the SAT problem asks: "Given a Boolean formula, is there a truth-value assignment such that it evaluates to True?". The corresponding counting problem, called #SAT, asks: "Given a Boolean formula, how many truth-value assignments are there such that it evaluates to True?". And in general, the counting problem corresponding to a decision problem X is called #X, where # is the number sign. Counting complexity techniques have significant applications in clarifying the relation between complexity classes of P, NP, PH, etc, in circuit complexity, and in interactive proof systems.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.