Lesson plan

Non-constructive algorithm existence proofs

The vast majority of positive results about computational problems are constructive proofs, i.e., a computational problem is proved to be solvable by showing an algorithm that solves it; a computational problem is shown to be in P by showing an algorithm that solves it in time that is polynomial in the size of the input; etc. However, there are several non-constructive results, where an algorithm is proved to exist without showing the algorithm itself. Several techniques are used to provide such existence proofs.

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Article summary

The vast majority of positive results about computational problems are constructive proofs, i.e., a computational problem is proved to be solvable by showing an algorithm that solves it; a computational problem is shown to be in P by showing an algorithm that solves it in time that is polynomial in the size of the input; etc. However, there are several non-constructive results, where an algorithm is proved to exist without showing the algorithm itself. Several techniques are used to provide such existence proofs.

Key claims

  1. publication date: 1982 — source: Wikipedia · confidence 0.95

Discussion questions

  1. Summarise the article in your own words. Which single claim would you verify first, and why?
  2. The record states that the publication date is "1982". What evidence would count against this claim?
  3. Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
  4. If two sources disagreed about one of these facts, what would you need in order to trust one over the other?

Bibliography

  1. Wikipedia https://en.wikipedia.org/w/index.php?oldid=1322626215

Key claims and bibliography are generated from the same tracked claims and sources as the article page.