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Questions tagged [complexity-theory]

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7
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1answer
95 views

Why is the “general notion of a reduction […] inherent to the notion of self-reducibility”?

While reading "Computational Complexity: A Conceptual Perspective" by Oded Goldreich, I have come across the following passage, which I simply cannot get my head around: Note that the general ...
6
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0answers
86 views

Small universal monotone Turing machines

This paper surveys small universal Turing machines. What are some examples of small universal monotone Turing machines, as described by Schmidhuber? Which of these are efficient (polynomial time) ...
-1
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1answer
131 views

A conceptual question regarding hardness proofs by reduction [closed]

If we restrict the input domain of a known NP-hard problem P so that this restricted domain is equal to the input domain of another problem S, then show that we can reduce a solution to P given input ...
7
votes
2answers
336 views

Is there an algorithm which gets incrementally “smarter” as it runs?

Mind the following program: n = 0 best = 0 while (true): if (hash(n) > best): best = hash(n) ++n If you leave this program running for 10 years, when ...