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Problem Detail: I am reading about dependent types theory in the Homotopy Type Theory online book. In section 1.3 of the Type Theory chapter, it introduces the notion of hierarchy of Universes: $mathcal{U}_0 : mathcal{U}_1 : mathcal{U}_2 : cdots$, where every Read More …

Problem Detail: If the clock shows 14:15:36.909302, why not just use the fractions of a second part (09302) as a kind of random number? What is wrong with this form of generating random numbers? I am aware that obtaining truly random Read More …

Problem Detail: There is a time series of say $100$ data points. I wish to assign symbols of $0, 1, 2$ for each unique data point. The issue is I have tried but got stuck since no matter I specify the Read More …

Problem Detail: When we would like to prove lower bound comparison algorirthm, we often use decision tree, for example sorting by comparisons. So let’s consider find minimum in array $a[1..n]$ by comparison. Lower bound for that problem is commonly known – Read More …

Problem Detail: I was reading about decision problem. I understand that decision problem tell yes/no answer for an input. The decision is based on a decision procedure also called an algorithm. The wikipedia says that It is traditional to define the Read More …

Problem Detail: I suppose the calculation should not be done by only two factors (average reading speed/words per minute, and word count). But at least by a third parameter, that in my opinion should measure the difficulty of the used vocabulary Read More …

Problem Detail: Consider the following dinner party problem: Given a list of acquaintances, and a list containing all pairs of individuals who are not on speaking terms with each other, find the largest set of acquaintances you can invite to a Read More …

Problem Detail: I want to express the following constraint, in an integer linear program: $$y = begin{cases} 0 &text{if } x=0 1 &text{if } xne 0. end{cases}$$ I already have the integer variables $x,y$ and I’m promised that $-100 le x Read More …

Problem Detail: I want to study theory of computation on my own, so I am looking for books. What set of books would you recommend for the equivalent of a one-semester course that introduces theory of computation? Please post answers that Read More …

Problem Detail: Let $text{NOT-SELF} = {langle M rangle : M text{ is a TM that does not accept } langle M rangle }$. How do you prove the following claim? If $Q$ is a TM so that $L(Q) subseteq text{NOT-SELF}$, prove Read More …