Questions tagged [diagonalization]

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Can the diagonal language be empty?

We defined the diagonal language as follows in the lecture: \begin{align*} L_{\text{diag}}=\left\{w \in \left\{0, 1\right\} ^{*}\mid w=w_{i} \text{ for some }i \in \mathbb{N} \text{ and }M_{i} \text{ ...
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1answer
64 views

Can you diagonalize a language out of CSL?

In recursion theory, it is possible to diagonalize a computable function out of the class of primitive recursive functions. Can you do the same with context-sensitive languages? I was thinking we ...
2
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1answer
141 views

Proving FPT is strictly contained in XP

In their book Fundamentals of Parameterized Complexity, Downey and Fellows claim (in chapter 27.1) that $\mathrm{FPT}\subsetneq \mathrm{XP}$, and that this is a "basic result" that follows ...
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1answer
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M does not accept [M] | 'Correction' of proof possible?

The language $D=\{[M]|M([M])=0\}$ is not decidable because of the following argument: Suppose there was a $TM \space M_D$ that decides $D$. Then if we gave $M_D \space [M] $, there would be two ...
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0answers
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The role of diagonalization - asymmetry between TM and Recursion Theory

This might be a slightly strange or irrelevant question. My apologies if it is. I'll try to formulate it the best I can. First, here is an hypothesis: diagonalization is syatematically used to prove ...
1
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1answer
148 views

Hilbert's Hotel for guests with infinite string name

I was watching this video How An Infinite Hotel Ran Out Of Room, by Veritasium. The video says that it is not possible to fit names made of infinite strings of $\{A,B\}$. We know we can fit infinite ...