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I am analyzing two functions that are defined in terms of an effective enumeration $(M_n)_{n \in \mathbb{N}}$ of all Turing machines. For a given input $x$, the notation $M_n(x) \downarrow$ means that …

Suppose that we have a Turing Machine that can only move for multiples of n cells at a time. In other words it can jump from one cell to another with jumping $n, 2n, 3n$, and so on with a single move. …

I had a question if this is possible to prove: Prove for every graph G=(V,E), that if every vertex v∈V has deg(v)≥((n+1)/2) then G is 2-connected. i tried by using the theorem that if every vertex has …

Is there an efficient algorithm to find the approximate LCM of a list of reals? More precisely, given an epsilon, find the least L such that it is atmost epsilon away from a multiple of each real in t …

I am reading Computer Science Distilled book and in section 2.2 The Big-O Notation there is a line. A function with fastest-growing term of $2^n$ or weaker is $O(2^n)$ What does weaker mean here? Al …

As we know that there is a difference between "inclusive or" and "exclusive or" same way can we explain the difference between "inclusive and" and "exclusive and".

According to the first chapter of the HoTT book, dependent functions beget products: $$ (x : A) \rightarrow B\,x \equiv: \prod_{x : A} B\,x $$ of which $A \times B$ is a special form ($A \times B \con …

There is a theorem that said for every nondeterministic Turing machine that runs in $O(n^k)$ there is an equivalent deterministic Turing machine that runs in $O(2^{n^k})$. From this theorem, I underst …

When dealing with floating point numbers, is there every a time when adding two non-negative, finite, non-NaN numbers will result in a result that is less than the greater of the two? x + y < max(x, y …

I have been trying to solve a question that says in a directed graph with n vertices and m edges whose weights are all positive integers, we have specified two of them, namely $a$ and $b$. We want to …

Instead of doing a quicksort, you can store everything in a map. Because the map is alphabetical it's already sorted. It seems like instead of doing a quicksort you could instantly put everything in a …

On a recent job interview, I was asked the following question: A conveyer belt at a factory carries wooden planks. Planks are placed with spaces between them (length of spaces can vary). Each plank is …

I can't identify the language generated by the following grammar, $$S \rightarrow aSb \ | \ bSa| \ \epsilon $$ Based on my understating of CFGs, the language generated would be $L(G) = (L_1 + L_2 + L …

Given that there are variables x1, x2, x3, and y, I know that x1, x2 are positively correlated with y, while x3 is negatively correlated with y, but the specific quantitative relationships are unknown …

I have the language: G = {<B,w> | B is an oracle TM and B[ATM] accepts w} I need to prove if this language is decidable relative to ATM. How would I go on about doing that?? My idea was to build a mac …