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Is there a decision problem with a time complexity of Ө(n²)?

In other words, I'm looking for a decision problem for which the best known solution has been proven to have a lower bound of N².

I thought about searching for the biggest number in matrix but the problem is that matrix is an input of O(n²) so the solution is linear.

It doesn't need to be known problem, a hypothetical one would suffice as well.

EDIT I looking for a regular programing problem - not a Turing Machine.

It's could be an arrays, strings, graph etc.

Jon Hameratesh
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1 Answers1

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Yes: Checking that a string is a palindrome takes $\Omega(n^2)$ on a single tape Turing machine.

In general the time hierachy theorem implies that there are such problems for most reasonable functions.

For RAM, edit distance can't be solved in $O(n^{2-\epsilon})$ for $\epsilon > 0$ unless the strong exponential time hypothesis is false.

adrianN
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