# Tagged Questions

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### An established proof in Wang Tile which I doubt

When I was reading the paper: Wang, Hao. "Notes on a class of tiling problems." Fundamenta Mathematicae 82.4 (1975): 295-305. from http://matwbn.icm.edu.pl/ksiazki/fm/fm82/fm82119.pdf I could not ...
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### Is the solution bounded Diophantine problem NP-complete?

Let a problem instance be given as $(\phi(x_1,x_2,\dots, x_J),M)$ where $\phi$ is a diophantine equation, $J\leq 9$, and $M$ is a natural number. The decision problem is whether or not a given ...
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### Why relativization can't solve NP !=P?

If this problem is really stupid, please close it. But I really wanna get some answer for it. And I learnt computational complexity by reading books only. When I learnt to the topic of relativization ...
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### Quantum computation implications of (P vs NP) [duplicate]

Possible Duplicate: What impact would P!=NP have on the characterization of BQP? Before I begin, I had a similar post closed for mentioning the recently released (to be verified) proof that ...
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### What impact would P!=NP have on the characterization of BQP?

Many complexity theorists assume that $P\ne NP.$ If this is proved, how would it impact quantum computing and quantum algorithms? Would the proof immediately disallow quantum algorithms from ever ...
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### Decidable but nonrecursive sets

Until recently, I believed that recursive=decidable, subscribing to this Wikipedia quote: "In computability theory, a set is decidable, computable, or recursive if there is an algorithm that ...
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### Structure theorems for Turing-decidable languages?

Languages decidable by weak models of computation often have certain necessary characteristics, e.g. the pumping lemma for regular languages or the pumping lemma for context-free languages. Such ...
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### Completeness, easiest, hardest problems

One says that a language $L$ is complete for a complexity class $\mathcal{C}$ if $L$ is in $\mathcal{C}$ and every language in $\mathcal{C}$ is reducible to $L$. Thus, in a sense, $L$ is the hardest ...
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### Given a polynomial-time algorithm, can we compute an explicit polynomial time bound just from the program?

Question. Given a Turing-machine program $e$, which is guaranteed to run in polynomial time, can we computably find such a polynomial? In other words, is there a computable function $e\mapsto p_e$, ...
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### The problem of finding the first digit in Graham's number

Motivation In this BBC video about infinity they mention Graham's number. In the second part, Graham mentions that "maybe no one will ever know what [the first] digit is". This made me think: Could ...