Lesson plan
Gap theorem
:See also Gap theorem (disambiguation) for other gap theorems in mathematics. In computational complexity theory, the gap theorem, also known as the Borodin–Trakhtenbrot gap theorem, is a major theorem about the complexity of computable functions. It essentially states that there are arbitrarily large computable gaps in the hierarchy of complexity classes. For any computable function that represents an increase in computational resources, one can find a resource bound such that the set of functions computable within the expanded resource bound is the same as the set computable within the original bound. The theorem was proved independently by Boris Trakhtenbrot and Allan Borodin. Although Trakhtenbrot's derivation preceded Borodin's by several years, it was not known nor recognized in the West until after Borodin's work was published.
Article summary
:See also Gap theorem (disambiguation) for other gap theorems in mathematics. In computational complexity theory, the gap theorem, also known as the Borodin–Trakhtenbrot gap theorem, is a major theorem about the complexity of computable functions. It essentially states that there are arbitrarily large computable gaps in the hierarchy of complexity classes. For any computable function that represents an increase in computational resources, one can find a resource bound such that the set of functions computable within the expanded resource bound is the same as the set computable within the original bound. The theorem was proved independently by Boris Trakhtenbrot and Allan Borodin. Although Trakhtenbrot's derivation preceded Borodin's by several years, it was not known nor recognized in the West until after Borodin's work was published.
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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?
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