# Questions tagged [polynomial-time]

Use for algorithms, algorithm-analysis and complexity-theory questions that aim for polynomial running time resp. time complexity. Such questions often are are reference-requests or about runtime-analysis or time-complexity.

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### What is wrong with this argument that if A is NP Complete, but B is in P, then A\B is NP Complete and B\A is NP Complete as well?

The following seems to me to be relevant to this question, but to me is an interesting exercise, especially since I have not formally worked with complexity before, but I want to learn more: Suppose ...
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### Satisfiable CNFs where each clause contains logarithmically many different literals

Studying for my finals in Complexity theory. This question comes up in different variants and it requires to use probability. A side note before, to be more clear: A CNF clause consists of $n$ clauses ...
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### "Polynomial Counter" Turing Machine

I need some help with this question: Definition: A Turing-machine that is a counter for the language $L$ is called 'polynomial counter' if there exists a polynomial $p$ s.t. every word $w\in L$ ...
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### What is the difference between saying there is no ϵ>0 such that a problem can be solved in $O(n^{2-\epsilon})$ time and $n^{2-o(1)}$ or $\Omega(n^2)$?

I have seen the formulations there is no ϵ>0 such that a problem can be solved in $O(n^{2-\epsilon})$ time a problem requires time $n^{2-o(1)}$ a problem requires time $\Omega(n^2)$ being used ...
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### Why we can't have some algorithm to be polynomial if there are generic conditions that make them so?

I explain it better: There are some algorithms that is clearly in NP, also NP-complete, but that under certain conditions they can be solved in polynomial time. An example is Bin Packing, the decision ...
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### Reconstructing an Array via Time-Intensive Subset Queries

I am trying to design an algorithm for a problem, and the following is an auxiliary problem for which a good solution would imply a faster algorithm for the original problem. I am given access to an ...
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### Relations between deciding languages and computing functions in advice machines

I'm trying to understand implications of translating between functions and languages for P/Poly complexity. I'm not sure whether the following all makes sense. Giving it my best shot given my current ...
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### Global-input-local-output p-time algorithms

Are there polynomial-time algorithms whose input is global but output is local in nature? What I have in mind is a problem instead of an algorithm. It’s the satisfiability (SAT) problem. Each clause ...
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### Can we decide if a number is a power of any given $K$ in polynomial-time?

It is simple to decide powers of 2 in $O(n)$ time because it's just "0-bit Unary" after bit-1. (eg. $1000$ is a power of 2 in binary). I haven't found many other trivial powers of $K$ that ...
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### Given arbitrary integers of $K$ and $M$, can deciding $2^K$ + $M$ is a prime be in $P$?

Given arbitrary integers of $K$ and $M$, is $2^K$ + $M$ a prime? ...