Lesson plan
Proper complexity function
A proper complexity function is a function f mapping natural numbers to natural numbers such that: * f is nondecreasing; * there exists a k-string Turing machine M such that on any input of length n, M halts after O(n + f(n)) steps, uses O(f(n)) space, and outputs f(n) consecutive blanks. If f and g are two proper complexity functions, then f + g, fg, and 2 f are also proper complexity functions. Similar notions include honest functions, space-constructible functions, and time-constructible functions.
Article summary
A proper complexity function is a function f mapping natural numbers to natural numbers such that: * f is nondecreasing; * there exists a k-string Turing machine M such that on any input of length n, M halts after O(n + f(n)) steps, uses O(f(n)) space, and outputs f(n) consecutive blanks. If f and g are two proper complexity functions, then f + g, fg, and 2 f are also proper complexity functions. Similar notions include honest functions, space-constructible functions, and time-constructible functions.
Key claims
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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.